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Detection, channel estimation and interference suppression for DS-UWB Li, Jingjun 2007

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Detection, Channel Estimation and Interference Suppression for DS-UWB by LI, JINGJUN A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF APPLIED SCIENCE in T H E FACULTY OF G R A D U A T E STUDIES (Electrical and Computer Engineering) T H E UNIVERSITY OF BRITISH COLUMBIA September 2007 © LI, JINGJUN 2007 Abstract Ultra-wideband wireless transmission has attracted considerable attention as future technology for Wireless Personal Area Networks (WPAN). One of the proposals for standardization of a UWB physical layser is based on direct-sequence UWB (DS-UWB). The DS-UWB proposal envisages two modulation formats: binary phase shift keying (BPSK) and 4-ary bi-orthogonal shift key-ing (4BOK). Any DS-UWB compliant device is required to be able to transmit and receive BPSK signals. Due to the large transmission bandwidth, the UWB channel is characterized by a long delay spread which results in severe intersym-bol interference for UWB communications. We therefore study equalization for DS-UWB systems employing BPSK modulation. Since the equalization schemes use UWB channel information, which is not always available in prac-tical applications, we also study channel estimations for DS-UWB systems. Furthermore, DS-UWB systems can be interfered with by other unknown DS-UWB systems as well as other relatively narrow-band wireless communication systems that operate in the same band as DS-UWB systems and have a power spectral density (PSD) much stronger than that of DS-UWB systems. We therefore focus our attention on interference suppression for DS-UWB systems. In the first part of this work, we consider equalization for DS-UWB with BPSK modulation. We analyze the performance limits applicable to any equalizer, taking into account practical constraints such as receiver filtering and sampling. Our results show that chip-rate sampling is sufficient for close-to-optimum per-formance. For analysis of suboptimum equalizer strategies, we derive linear equalization schemes for DS-UWB systems. Moreover, we devise equalization ii schemes with widely linear processing, which improve performance without increasing equalizer complexity. Simulation and numerical results show that low-complexity (widely) linear and nonlinear equalizers perform close to the pertinent theoretical limit. Finally, to ease the complexity of practical hard-ware implementation, we derive two low-complexity finger selection schemes for DS-UWB systems and compare their computational costs. Equalizers based on a limited number of fingers with finger selection schemes can achieve perfor-mance close to that of equalizers with all fingers within the processing window. In the second part, we investigate channel estimation for DS-UWB systems. To this end, we first study blind channel estimation methods. The simulation results indicate that blind estimation methods are not applicable because of the long delay spread nature of UWB channels. Therefore, training-based channel estimation is preferred. We further derive a low-complexity channel estima-tion method using training sequences. The simulation and numerical results show that the proposed training-based channel estimation is highly appropriate for practical implementation because it can achieve performance close to the theoretical limit while at the same time causing only little bandwidth wastage. In the third part, we study interference suppression for DS-UWB systems. We first devise structures and methods for interference suppression. In this context, we develop new adaptive filters to remove the multiple-access inter-ference (MAI) by other unknown DS-UWB users or unknown narrow-band interferers (NBI). If the information of NBI is available at the receiver, we propose another filter with a simple structure to largely eliminate the impact of NBI. Simulation and numerical results show that the proposed adaptive filters can effectively suppress interference with moderate computational com-plexity. The narrow-band interference can be almost entirely removed with the a simple band-stop filter even when the interference power is very large. iii Contents Abstract ii Table of Contents vi List of Tables vii List of Figures x List of Abbreviations and Symbols xi Acknowledgements xiv 1 Introduction 1 1.1 Ultra-wideband Technology 2 1.2 DS-UWB Proposal for W P A N Physical Layer Standard 3 1.3 Challenges and Motivation 4 1.4 Contributions 7 1.5 Thesis Organization 8 2 DS-UWB Transmission System 10 2.1 BPSK Transmission Model 10 2.2 Channel Model 11 2.3 Receiver 14 2.4 Signal Model 15 3 Equalization Strategies and Finger Selection Schemes for Single User 19 3.1 Equalization Strategies 19 iv 3.1.1 Linear Equalization (LE) 20 3.1.2 Decision Feedback Equalization (DFE) 20 3.1.3 Widely Linear Counterparts 21 3.2 Finger Selection Algorithms 23 3.2.1 Greedy Algorithm 24 3.2.2 Simulated Annealing 25 3.3 Simulation Results and Discussion 28 3.3.1 Simulation Parameters 28 3.3.2 Simulation Results for Equalization Schemes 29 3.3.3 Simulation Results for Finger Selection Schemes 34 4 Channel Estimation for a Single DS-UWB User 45 4.1 Blind Channel Estimation 45 4.2 Training-Based Channel Estimation 48 4.3 Complexity Comparison between the M P C and other Channel Estimation Algorithms 50 4.4 Results and Discussions 51 4.4.1 Simulation Results for the Blind Channel Estimation . . 51 4.4.2 Simulation Results for Channel Estimation with Train-ing Sequences 53 5 Interference Suppression 63 5.1 WL-LMS Algorithm 64 5.2 W L - M O E Algorithm 65 5.3 Two-stage Adaptive Filter 67 5.4 Narrow Band Interference 68 5.5 Simulation Results and Discussions 71 5.5.1 MAI Suppression 71 5.5.2 NBI Suppression 75 6 Conclusions 80 Appendices 83 v A Derivation of SINRs for Equalization Schemes vi List of Tables 3.1 Pseudo-code for simulated annealing heuristic 27 3.2 Parameters for the considered BPSK DS-UWB systems 28 4.1 Complexity comparison for channel estimation algorithms. . . . 51 vii List of Figures 2.1 Block diagram of BPSK DS-UWB transmission system 11 2.2 Impulse response of a sample realization for channel scenarios . 13 2.3 Illustration of equivalent system for a DS-UWB systems with K users, processing window of 4 bit duration 17 3.1 B E R versus 10 log10{Eb/N0) for linear MMSE CM1 and N = 24. Also shown MFB1 and 2 [10] 29 3.2 BER versus 101og1 0(E6/JV0) for linear MMSE and D F E CM4 and N = 24. Also shown MFB1 and 2 [10] 30 3.3 B E R versus 101og1 0(£6/AT0) for linear MMSE and D F E CM4 and N = 6. Also shown MFB1 and 2 [10] 31 3.4 B E R versus 10log10(Eb/N0) for Linear MMSE and W L M M S E CM4 and N = 24. Also shown MFB1 and 2 [10] 32 3.5 B E R versus 10 log 1 0 (£ 6 /AT 0 ) for linear MMSE and W L MMSE CM4 and N = 6. Also shown MFB1 and 2 [10] 33 3.6 Average SINR loss as function of number of fingers for the three scenarios(CMl, N = 24), (CM4, N = 24) and (CM4, N = 6) at SNR=14dB 34 3.7 B E R versus 101og10(Eb/A^0) using the G A for CM1, JV = 24. . . 35 3.8 B E R versus 10Tog10(£76/W0) using the G A for CM4, N = 24. . . 36 3.9 B E R versus 101og 1 0(£ 6/Ar 0) using the G A for CM4, N = 6. . . . 37 3.10 B E R performance comparison for 4 equalization schemes with Greedy Algorithm (GA) for CM4, N=6 38 3.11 B E R performance comparison between Strongest Paths (SP) method and Greedy Algorithm (GA) for CM4, N = 6 39 viii 3.12 Average SINR loss as function of number of fingers for the SP and the GA for CM4, N — 6 40 3.13 Average SINR gain as function of search space used by Sim-ulated Annealing for selecting 16 fingers with initial state ob-tained by SP method, for CM4, N = 6 at SNR=14dB 41 3.14 B E R versus 10 \ogw(Eb/N0) of the GA and R A K E combining [13] for CM4, N = 24 42 3.15 B E R versus 10log1Q(Eb/N0) of the G A and R A K E combining [13] for CM4, N = 6 43 4.1 B E R versus 101og1 0(E f c/A / 0) for Blind Channel Estimation for CM4 and N=2A 52 4.2 BER versus 10 log10(Eb/N0) for channel estimation with train-ing symbols of different length for CM4 and N=2A 53 4.3 B E R versus 10logw(Eb/No) for channel estimation with train-ing symbols of different length for CM4 and A^=6 54 4.4 SINR of M P C algorithm versus number of training symbols of different length for CM4 and N=24 at SNR = 14dB 55 4.5 Channel estimation error of M P C algorithm versus number of training symbols of different length for CM4 and N=24 at SNR = 14dB 56 4.6 SINR of M P C algorithm versus number of training symbols of different length for CM4 and N = 6 at SNR = 14dB 57 4.7 Channel estimation error of the M P C algorithm versus number of training symbols of different length for CM4 and N = 6 at SNR = 14dB 58 4.8 B E R versus l0logw(Eb/N0) for channel estimation with the M P C algorithm with 100 training symbols, finger selection by the GA, for CM4 and N = 24 59 4.9 B E R versus 10\og1Q(Eb/N0) for channel estimation with the M P C algorithm with 200 training symbols, finger selection by the GA, for CM4 and N = 6 60 ix 4.10 B E R versus 10 log10(-E(,/./Vo) comparison for channel estimation with the M P C algorithm with 100 training symbols for CM4 and N — 24, comparison is made between L E and W L E , finger selection with the GA. Also shown: B E R performance of L E and W L E of exact channels 61 4.11 B E R versus 101og10(Ei,/A^0) comparison for channel estimation with the M P C algorithm with 200 training symbols for CM4 and N = 6, comparison is made between L E and W L E , finger selection with the GA. Also shown: B E R performance of L E and W L E of exact channels 62 5.1 Structure of two-stage filter 68 5.2 Spectrum crossover of the NBI in UWB systems 69 5.3 Receiver with Bandstop filter for NBI suppression 70 5.4 B E R versus 10 \ogw(Eb/N0) for MAI suppression for CM4, N = 24 71 5.5 B E R versus 10 logw(Eb/N0) for MAI suppression for CM4, N = 6. 72 5.6 SINR versus number of iterations for MAI suppression for CM4, AT = 24 at SNR = 14dB 73 5.7 SINR versus number of iterations for MAI suppression for CM4, JV = 6 at SNR = 14dB 74 5.8 B E R versus 10 logw(Eb/NQ) for single NBI suppression for CM4, N = 24 75 5.9 B E R versus 10 \og10(Eb/N0) for single NBI suppression for CM4, N = 6 76 5.10 B E R versus 10 \ogw(Eb/N0) for NBI suppression with band-stop filter for CM4, N=24. 77 5.11 B E R versus 10 logw(Eb/No) for NBI suppression with band-stop filter for CM4, N = 6 78 x List of Abbreviations and Symbols Acronyms AWGN Additive White Gaussian Noise B E R Bit Error Rate BPSK Binary Phase-shifting Keying C D M A Code Division Multiple Access DARPA Defense Advanced Research Projects Agency D F E Decision-Feedback Equalization DS Direct Sequence F B F Feedback Filter FCC Federal Communications Commission F F F Feed-Forward Filter GA Greedy Algorithm ISI Intersymbol Interference ISM Industrial, Scientific and Medical xi LMS Least Mean Square LOS Line Of Sight MAI Multiple Access Interference M F B Matched Filter Bound M O E Minimum Output Energy NBI Narrowband Interference NLOS Non Line Of Sight O F D M Orthogonal Frequency Division Multiplexing PAR Peak to Average Ratio PCS Personal Communications Service RLS Recursive Least Square SA Simulated Annealing SINR Signal to Interference and Noise Ratio SNR Signal to Noise Ratio SP Strongest Paths SVD Singular Value Decomposition UMTS Universal Mobile Telecommunication System UWB Ultra-wideband W D F E Widely-Linear Decision-Feedback Equalization W L Widely Linear W L E Widely Linear Equalization W P A N Wireless Personal Area Network xii 4 B 0 K 4 Binary bi-orthogonal Keying Operators and Notation argmax{-} Argument maximizing the expression in the bracket argmin{-} Argument minimizing the expression in the bracket | • | Absolute value of a complex number * Convolution In x Natural logarithm of x Re{-} Real part of a complex number <5(-) Dirac delta function || • || Frobenius norm sign{-} Sign of a real number E{-} Expectation [•]* Complex conjugate [•]T Matrix or vector transposition [•]H Matrix or vector Hermitian transposition Im Identity matrix with dimension m x m xiii Acknowledgments I would like to express my gratitude to Dr. Cyril Leung for stimulating sug-gestions and encouragement that helped me in all the time of research and writing of this thesis. I am also deeply indebted to Dr. Lutz Lampe for help-ing to supervise me, providing resources and subjects, and offering direction and penetrating criticism. I would also like to extend my sincere thanks to Dr. Robert Schober for his valuable discussions on widely linear processing. Especially, I would like to give my special thanks to my wife Mei whose patient love enabled me to complete this work. Lastly, and most importantly, I wish to thank my parents. They bore me, raised me, supported me, taught me, and loved me. To them I dedicate this work. xiv Chapter 1 Introduction The last decade has witnessed a rapid development in wireless communica-tions. Communication has changed from fixed place-to-place communications to wireless mobile person-to-person communications. The widespread adop-tion of wireless communications was accelerated as governments throughout the world provided increased competition and new radio spectrum licenses for personal communications services (PCS). The next generation of wireless communications networks are being designed to facilitate high speed data com-munications traffic in addition to voice calls. Wireless networks have been increasingly used as a replacement for wires within homes, buildings, and of-fice settings through the deployment of wireless local area networks (WLANs). The Bluetooth technology has replaced troublesome appliance communication cords with invisible wireless connections within a person's personal workspace by providing data rates of up to 1 Mbps using the 2.4 GHz Industrial, Sci-entific and Medical (ISM) band [1]. However, the growing demand for much higher data rates has given rise to the need for new reliable wireless tech-nologies enabling robust, low cost and low power devices. With the approval of its application for commercial purposes in the United States and similar regulatory processes currently under way in many countries worldwide, the ultra-wideband (UWB) technology is anticipated to suitably meet the increas-ing demand in wireless networking and to dominate the market place. 1 1.1 Ultra-wideband Technology Ultra-wideband (UWB) radio communications systems operate by using as signaling waveforms, baseband pulses of very short duration, typically on the order of a nanosecond (ns) or less. UWB pulses were first produced, in the late 1890s, using spark gap transmitters by Gugliemo Marconi, and were used to transmit Morse code across the Atlantic in 1901 [2]. The potential of pulse based UWB technology for use in radars and communications was realized in the 1960s and 70s from the study of electromagnetic-wave propagation as viewed from the time-domain perspective [2], [3]. The term " Ultra-wideband" was first used in 1989 by the Defense Advanced Research Projects Agency (DARPA), for differentiating impulse based radars from conventional ones [2]. Until recently, this technology was restricted for use in defense applications such as radars and covert communications. The advances in semiconductor devices and microprocessors in the last few years, along with a more in-depth understanding of UWB system characteristics, have made it possible to build commercial applications based on UWB technology. A UWB signal is defined to be one that possesses an absolute bandwidth larger than 500 MHz or a relative bandwidth larger than 20% and can coexit with incumbent systems in the same frequency range due to its large spreading fac-tor and low power spectral density. In the U.S., the Federal Communications Commission (FCC) issued First Report and Order [4] in February 2002, ap-proving commercial use of UWB devices in the 3.1 - 10.6 GHz band with strict limits on power emission levels to allow co-existence of UWB systems with other wireless communication systems such as IEEE 802.11a W L A N , Univer-sal Mobile Telecommunication System (UMTS) and Global Positioning System (GPS). The FCC spectral mask allows communication devices to use 7.5 GHz of bandwidth between 3.1 GHz and 10.6 GHz, with a power spectral density not exceeding -41.3 dBm/MHz. Thanks to its wide-bandwidth, UWB technology allows for the possibility of 2 very high data rates even at relatively low signal to noise ratio (SNR). However, due to FCC power restrictions the high data rate UWB devices can operate only over short ranges (less than 10 m). UWB devices are intended to operate in the 3.1 - 10.6 GHz band, on a license free basis, without causing harmful interference to existing radio systems, thereby increasing the spectrum utiliza-tion. UWB has many desirable properties such as robustness to fading and multipath diversity, making it ideal for a variety of applications such as short-range high-speed data transmission and precise location estimation. In the last few years, UWB has attracted considerable attention from industry. Technology leaders such as Motorola, Texas Instruments, Mitsubishi and Gen-eral Atomics have already started development of UWB based W P A N devices capable of providing data rates up to 500 Mbps. 1.2 DS-UWB Proposal for WPAN Physical Layer Standard The DS-UWB standard proposal [6] specifies two bands of operation: the lower band occupies 1.75 GHz of spectrum from 3.1 GHz to 4.85 GHz and the higher band occupies 3.5 GHz of spectrum from 6.2 GHz to 9.7 GHz. Each band sup-ports up to six piconets. Any DS-UWB compliant device is required to support piconet channels 1-4, that lie in the lower band. Support for piconets 5-6 in the lower band and 7-12 in the upper band is optional. A fixed chip rate and a fixed center frequency are specified in the proposal for each of these 12 piconets. Spreading codes of various lengths may be used to support different data rates. The DS-UWB standard proposal specifies the use of binary phase-shift keying (BPSK) or 4-binary bi-orthogonal keying (4BOK) to modulate the data sym-bols. Any DS-UWB compliant device must be able to transmit and receive BPSK signals, and to transmit 4BOK signals. However, the ability to receive 4BOK signals is optional. The proposal specifies the use of square root raised 3 cosine (SRRC) pulse shaping. Use of convolutional codes of rate 1/2 and 3/4 is specified, to provide forward error correction. In order to reduce the sensi-tivity of the convolutional codes to error bursts, convolutional interleaving is used. In our work, we focus on detecting BPSK signals in DS-UWB systems and do not consider the effect of convolutional coding and interleaving. 1.3 Challenges and Motivation The multipath resolution of a signal that propagates over a channel is defined as the minimum delay between two paths that can be distinguished at the receiver as individual multipath components, and is given by the inverse of the bandwidth occupied by the transmitted signals. Al l the multipath com-ponents separated by more than the pulse duration can be resolved as indi-vidual paths with distinct propagation delays, whereas multipath components arriving within the resolution time of received signal cannot be resolved as individual paths and hence interfere constructively/destructively, resulting in fading. The very fine resolution provided by UWB due to the short pulses duration (0.7 ns for DS-UWB systems in the lower band) offers advantages of robustness to fading and enhanced multipath diversity. Due to this very short duration of UWB pulses, fewer multipath components arrive within the resolution period, thereby reducing destructive interference and resulting in reduced signal fading. Moreover, a larger number of multipaths are resolvable, resulting in significant multipath diversity. Signal propagation in indoor UWB channels typically results in long root-mean-square (rms) delay spreads, thus resulting in significant ISI that spans a number of symbols. Minimum mean-square error (MMSE) equalizers have been proposed in [7] for detection because these low-complexity equalizers are able to effectively mitigate ISI as well as background noise. Equalization for DS-UWB has been addressed in a number of recent publica-4 tions. Typically, users in a DS-UWB system employ R A K E receivers to collect energy from different multipath components [8]-[10]. A maximum ratio com-bining (MRC) R A K E receiver is optimal scheme in the absence of interfering users and ISI. The use of MMSE equalizers at the output of MRC R A K E re-ceivers for ISI suppression is proposed in [10]. Equalization for DS-UWB of this structure is processed at the symbol-rate. However, due to the long delay spread nature of UWB channels, the combining scheme of R A K E receiver in [10] is not optimal. Therefore, we would like to investigate the performance of equalizations for DS-UWB with chip sampling. Since a UWB signal has a very wide bandwidth, the number of resolvable multipath components is usually very large. A receiver that combines all the paths of the incoming signal is not implemented in practice due to its com-plexity. Also, the hardware structure of the equalizers that follow the receiver will be relatively simple if they are built based on fewer number of paths. A feasible implementation of multipath diversity combining can be obtained using a receiver which combines the M best out of L multipath components [9], and [11]. A genetic-algorithm-based approach is proposed in [12] for path selection in Impulse Radio UWB systems. In [11], a path selection scheme is proposed that chooses the paths with highest signal-to-interference-plus-noise ratios (SINRs) for high data rate UWB systems. These works lead us to focus our research on path selections for DS-UWB systems that follow the proposed standard specifications in [6]. Detectors for DS-UWB systems often require the knowledge of channel pa-rameters such as the gain and propagation delay of each path component. If the channel state information is not known at the receiver, techniques for adapting the detectors have been proposed to effectively retrieve useful in-formation for the user in interest. In [16], a blind method is proposed for adapting the linear MMSE detector based on a signal subspace tracking tech-nique for CDMA, with prior knowledge of only the signature waveform of the 5 desired user. The Power-of-R (POR) technique is proposed in [17] to blindly estimate multipath parameters in a time-hopping (TH) UWB system. The multipath channel can also be estimated by transmitting a training sequence. For training-based channel estimation, [11] proposes Least Squares (LS) based channel estimation and Matching Pursuit (MP) based channel estimation for UWB systems. LS based channel estimation is computationally complex due to matrix inversion. MP based channel estimation, which is computationally more efficient, can achieve performance very close to LS based channel esti-mation. [18] introduces matching pursuit followed by a cancelation (MPC) algorithm for multipath channel estimation in C D M A . The cancelation step of the algorithm uses the already estimated channel tap to remove interfer-ence from the received vector in order to identify the channel coefficients more accurately. The application of a subspace tracking technique and M P C on DS-UWB, however, has not yet been explored. Therefore, in this work we aim at developing channel estimation schemes specific to BPSK DS-UWB systems that can effectively estimate the channels and at the same time provide a good performance-complexity tradeoff. The filter coefficients of linear receivers can be adapted to the channel and interference situation by using data-aided [19] or blind adaptive algorithms [20]. The performance of multiuser receivers can be improved if not only the received signals, but also their complex conjugates, are processed [21]. In [21], a data-aided widely linear least mean square (WL LMS) algorithm and a blind widely linear minimum-output-energy (WL MOE) algorithm for Multiple access interference (MAI) suppression for DS-CDMA are proposed. [22] intro-duces two-stage adaptive linear receivers for DS-CDMA, with the receivers consisting of the serial concatenation of data-aided and blind adaptive stages. Following [21] and [22], we would like to develop receivers with W L processing for DS-UWB to suppress interference. Coexisting with many concurrent narrowband services, the performance of 6 UWB systems will be affected considerably by them due to the high PSD of these narrow-band signals with respect to the UWB signals. Various methods to suppress these narrow-band interferences (NBI) for UWB systems have been presented. A Singular Value Decomposition (SVD) algorithm is introduced in [23] for NBI suppression in UWB systems. Involving matrix decomposition, this algorithm is not practical due to its complexity. Linear adaptive MMSE with RLS algorithm is applied in [24] to remove the negative effects of NBI on DS-UWB systems. However, this receiver structure is not recommended because of its high complexity caused by the application of RLS algorithm. Therefore, it is our goal to propose a low-complexity algorithm that can effec-tively suppress NBI. 1.4 Contributions • We introduce a discrete-time BPSK DS-UWB system model. Four clas-sic equalization schemes, namely Linear Equalization (LE), Decision-feedback Equalization (DFE), W L Equalization (WLE) and W L Decision-feedback Equalization (WDFE) are applied to the system model. W L equalization schemes achieve performance better than their "linear" coun-terparts while incurring the same or lower computational complexity. Greedy Algorithm (GA) and Simulated Annealing (SA) are investigated for finger selections. SA with the initial state generated by picking strong paths is discovered to achieve performance slightly better than GA, at the expense of additional computational cost. Depending on the under-lying UWB channel, the number of fingers to sufficiently capture the useful received energy varies between about 16 and 64. • We develop blind detection schemes [20] for symbol detection in DS-UWB systems. The only requirement for the blind detection scheme is the knowledge of the signature waveform for the desired user. The blind detection scheme, however, performs much worse than the optimal case in which exact channel state information is known, due to the long delay 7 spread nature of UWB channels. Therefore, we propose UWB channel estimation and equalization using training sequences. We develop an algorithm that can effectively estimate channel information and result in acceptable performance for DS-UWB systems with training symbols on the order of a hundred. The transmission of a training sequence for channel estimation does not cause much bandwidth wastage to DS-UWB systems due to the high data rate of UWB communications. • We develop two-stage W L LMS adaptive filters for both MAI and NBI suppression in DS-UWB systems. We show that this filter structure can achieve performance better than its linear counterpart while incurring a lower computational complexity. The two-stage W L LMS adaptive filters can largely eliminate the interference caused by the narrow-band inter-feres or unknown multiple access interferers, while converging rapidly to the corresponding steady-state. We also develop a simple but effective filter structure which can minimize the negative effect of NBI regardless the power of the interferences. Even in the worst case scenario, where the NBI occupies the entire operating band, this filter structure can still perform close to the case with no NBI. 1.5 Thesis Organization In Chapter 2, the DS-UWB transmission model is introduced. BPSK modu-lation scheme is briefly reviewed and the IEEE 802.15.3a channel model [25] is described. The receiver structure is also discussed. Various equalization schemes for DS-UWB are considered in Chapter 3, fol-lowed by a discussion of two finger selection schemes. The simulation results for equalization and finger selection schemes are presented in the final part of this chapter. In Chapter 4, blind channel estimation and equalization for DS-UWB is intro-8 duced. The performance of blind detection is then compared to the benchmark when perfect CSI is available at the receiver. Subsequently, we study channel estimation with the aid of training symbols. Performance results for channel estimation are the provided. In Chapter 5, MAI and NBI suppression for DS-UWB systems is studied. De-pending on the knowledge of the center frequency of the NBI, different inter-ference suppression structures are examined. Subsequently, simulation results are presented and discussed. Finally, in Chapter 6, we summarize contributions and the main finding of the thesis. We also make some suggestions for future work. 9 Chapter 2 DS-UWB Transmission System In this chapter, the transmission model for the DS-UWB system, which in-cludes the modulation scheme, the pulse shaping filter, the channel model, the receive input filter and the demodulator, is dicribed. In this work, an equiva-lent baseband transmission model, i.e., complex-valued signals and systems [5], is adopted. The transmission model follows the specifications in the DS-UWB physical layer proposal [6]. The BPSK DS-UWB model is briefly reviewed, and the IEEE 802.15.3a channel model [25] for UWB systems is described. This is followed by a discussion of the receiver structure for BPSK modulation schemes and the signal model. 2.1 BPSK Transmission Model The standard proposal [6] requires all DS-UWB systems to be able to trans-mit and receive BPSK modulated signals. Various data rates are achievable by direct sequence spreading of BPSK symbols, using spreading sequences of lengths varying from 1 to 24 chips (for more details see [6], Table 6-7]). The block diagram of the equivalent baseband system model for the BPSK DS-UWB system is shown in Fig. 2.1. At the transmitter, BPSK symbols a[k] are spread and modulated with the chip pulse gr{t)- The pulse shape is 10 Spreading code •m. Tr&sritf Filter, 8ri0 ' Channel-M O 'White "Gaussiah'Ndiie Equalizer. System' tiki ;Receive-Filt'er.r Figure 2.1: Block diagram of BPSK DS-UWB transmission system, defined as i V - 1 9(t)^J2c^9T(t-jTc), (2.1) where c[j] denotes the j th chip of the spreading code of length N and Tc is the chip duration. The pulse shaping filter gr(t) is SRRC [26] with a roll-off factor a = 0.3 [6]. Finally, the transmit signal s(t) can be written as oo a ( t ) = *[k]9{t-kTB), (2.2) k=—oo with symbol duration Ts = NTC. 2.2 Channel Model The channel model considered is the IEEE 802.15.3a model for UWB W P A N systems [25], [27]. It is based on the Saleh-Valenzuela model [28] with some modifications to account for the properties of measured UWB channels. Multi-path arrivals are grouped into two categories: cluster arrivals and ray arrivals within each cluster. The interarrival times between clusters or rays within a cluster are exponentially distributed. Lognormal fading is associated with clusters and also with rays within a cluster. The cluster and ray decay factors 11 are based on a given power profile. Finally, the entire impulse response under-goes lognormal shadowing. The impulse response of the multipath channel consists of Lc clusters of Kr rays and can be expressed as [25] • 5(t) denotes the Dirac-delta function. • Ti is the delay of the Ith cluster. • Tk,i is the delay of the kth multipath component relative to the Ith cluster arrival time T\. • (Xk,i is the multipath gain coefficient, where (Xk,i = Pk,i£i@k,i- The phase of ak,i is given by the term pk,i which can be +1 or -1 with equal prob-ability to account for signal inversion. & reflects the lognormal fading associated with the Ith cluster and @k,i is the lognormal fading associated with the kth ray of the Ith cluster. The variables £j and are char-acterized as: 20 l o g 1 0 ) ~ Normal(fj,k,i, o\ + cr|), where a\ and a\ are the standard deviations of the cluster and the ray lognormal fading term respectively. The term is given by where tto is the mean energy of the first path of the first cluster. T and 7 denote the cluster and ray decay factors, respectively. The total energy contained in the multipath gain coefficients for each realization is normalized to one. • X is the lognormal shadowing and is characterized as 201og1 0(X) ~ Normal(0,al), where a\ is the standard deviation of the lognormal fad-ing term for the total multipath realization. (2.3) i=i fc=i where (2.4) 12 Impulse response of CM1 Impulse response of CM4 Figure 2.2: Impulse response of a sample realization for channel scenarios Four different channel models (CMs) are specified in [25] with parameters de-signed to fit four different scenarios: CM1 for 0-4 m Line-of-Sight (LOS), CM2 for 0-4 m non-LOS (NLOS), CM3 for 4-10 m NLOS, and CM4 for NLOS with an extreme root-mean-square (rms) delay spread of 25 ns. The channel model parameters for the different channel scenarios are described in [25] and [27]. Figure 2.2 shows sample impulse responses for channels CM1 and CM4. The typical rms delay values range from 5 ns for channel CM1 to 25 ns for channel CM4 [25], [27], whereas the chip period is approximately 0.76 ns in the lower band and 0.38 ns in the higher band. This implies that the UWB channel behaves in a highly frequency selective manner for DS-UWB systems. Due to the very fine multipath resolution of DS-UWB signals, resulting from the short duration of DS-UWB signals, and long delay spreads associated with the UWB channel, a large number of multipaths can be resolved, thereby re-13 suiting in high multipath diversity. Since few multipath components arrive within one chip duration, DS-UWB signals do not undergo significant fading [2]. Moreover, this results in the total received energy being distributed among a large number of paths, however, not every resolvable multipath contains a significant amount of energy [27]. Al l these characteristics significantly impact the overall receiver design of DS-UWB systems as will be discussed in the fol-lowing sections. In the following, the equivalent baseband representation of h'c(t), denoted by hc(t), is considered. Consider an K-usev binary communication system, the total received complex baseband signal is the superposition of the signals from the K users, plus additive white Gaussian noise (AWGN), i.e. where Si(t) is the transmitted BPSK signal of user i, hc,i (t) is the equivalent baseband channel impulse response of user i, and nc(t) is an equivalent base-band AWGN process with two-sided power spectral density A^. As shown in Fig. 2.1, the receiver front-end consists of a matched filter with impulse response gn{t) = <7f (—*) followed by chip-rate sampling. Let Oi[k] (k = ...,-1,0,1,2,...) denote the bit stream of user i. The received signal r(t) after the matched filter is given by 2.3 Receiver K (2.5) K oo N-l (2.6) i=l fc=—oo j=0 where nR(t) = nc{t) * gR(t) (2.7) 14 is the filtered AWGN nc(t) and h,i (t) = gr(t) * hCn (*) * gR(t), (2.8) is the continuous-time overall impulse response including the effects of the transmitter filter, the equivalent complex baseband UWB channel for user i, and the receiver filter. { c j j l j ^ o 1 i s the signature sequence assigned to user i, and JVj is the processing gain of user i. Introducing the discrete-time overall impulse response of user i /k),i[«] = /io,i(KT c) ) (2.9) the discrete-time received signal after sampling at the chip rate 1/TC can be expressed as K oo iV -1 r ^ = S 5 Z °i[J]hon [K-kN- j] + nR[K], (2.10) i=l fc=—oo j'=0 where nR[K] = nR(nTc). (2.11) 2.4 Signal Model Intersymbol interference is expected at the UWB receiver due to the fact that the root-mean-square delay spread of the UWB channels is longer than the bit duration. Therefore, any decision made on a particular data symbol needs to take into account the decisions on previous and successive symbols and on the overlapping symbols of other users. Let Lcti denote the order of the impulse response /io,i[K] °f ^ n e discrete-time chip rate overall equivalent complex UWB channel of user i, that is, the length of /io,i[«] is Lc,i chip periods. We define the effective discrete-time chip rate spreading sequence of the ith user as ^ / [ « ] = ^ o , i M * c i > l < i < A ' (2.12) 15 where q is the signature assigned to the ith user. Notice that the length of h^f is Neff = Lc,i +N — 1 chip periods, that is, a transmitted DS-UWB symbol is spread over Neff chip periods due to the time dispersive nature of the channel. To utilize the energy in all multipaths, a sliding processing window of Nw (Nw > Neff) is applied for detection. It is convenient to view a DS-UWB system with parameters K and TV as an equivalent synchronous DS-UWB system with KeH = K\jf-~\ fictitious users with spreading sequences of length Nw [7]. Fig. 2.3 illustrates a simple case with a processing window crossing over 4 symbol durations [7]. In the example, without loss of generality the processing window is applied to detect User l's symbol transmitted at time K = 0. User 1 can be viewed an equivalent synchronous system with 4 effective users with spreading sequence of length of processing window. The desired user is the effective user #1 of Userl. The equivalent synchronous systems of other users can be built in a similar way. We now introduce a matrix model for a simple case where only one user is considered. This can be extended to a multi-user case. With only one user, (2.10) reduces to oo yv - i r[«] = aik\ S c\j]ho[K - k N - j] + TIR[K], (2.13) k——oo j—d where the user index has been omitted for simplicity. We need to form a signal vector r of Nw samples to detect one transmitted bit. We start this by grouping N received samples r[k] = [r[kN]}, ...,r[kN - (N - 1)]]T (2.14) Notice that r[k] can also be written as L r[k] = J2a[k-l}f_[l} + nR[k}, (2.15) 16 Pro&ssirig window [ i User 1 •C-l | «-3 ! | 1 User 2 | K=0 1 1 'K=2. • • • 1 ! ! UserK. 1 k=0. | K=l | k-2 | K=3 j | I 1 1 1 1 i •1 • - _ _ J ;Sym66l"durati6ri;'N cliips | J Effeerite #^iog-scqMeife«'j N«, chips \^X\^0^Xr€»,W€ii\ Effective*! forUser.1 I g g j g M j M M M i l Q | Effective *2 for User i | 0 l l g ^ ' ^ ^ ^ ^ g l 0 I Effective* for User .1 ' | 0 \"''*4^^iJ ' 'V ' ! I Effective «forUser.l | I) IjFXpW?.'^] Figure 2.3: Illustration of equivalent system for a DS-UWB systems with K users, processing window of 4 bit duration where L = [-^FJ, and N - l N - l fj] = E cUMlN - j], E c\j]ho[lN - j - N - 1}}T. (2.16) j=0 j=0 then r is formed by grouping (qf + 1) vectors f_[k] r = [rr[k],...,rr[k-qf]]T, (2.17) with Nw = N(q/ + 1). Actually r can have any size, does not need to be a multiple of N. Also, we form a (qf + L + 1) dimensional signal vector a a = [a[k],...,a[k - qf},...,a[k - (qf + L + l ] ] r . (2.18) 17 We further define the Nw x (qf + L + 1) matrix H of spreading sequence f[0] f[l] 0 f[0] f[L] 0 f [ L - l ] i[L] 0 0 H = 0 (2.19) 0 0 0 f[2] ... 0 f[l] ... f[L] and the Nw dimensional noise vector n. We can write the compact matrix For the multiple user case, (2.20) is changed to K i=l where rtotai is the total received signal, and H; and represent the transmis-sion matrix and signal vector of user i, respectively. relation r = Ha + n. (2.20) 18 Chapter 3 Equalization Strategies and Finger Selection Schemes for Single User 3.1 Equalization Strategies The classic Linear Equalization (LE) and Decision Feedback Equalization (DFE) are briefly reviewed in the context of DS-UWB. The minimum mean-square error (MMSE) criterion is applied for filter optimization [5]. W L pro-cessing for the BPSK DS-UWB are then introduced. For simplicity, we con-sider the case of one user, and all the equalization schemes are based on (2.20). Two matched filter bounds for the DS-UWB, namely MFB1 and MFB2 are obtained in [10]. For MFB1, it is assumed that all multipath energis can be captured and that the time duration between transmitted symbols is large enough so that no ISI occurs. MFB2 provides a lower bound on the error performance of any receiver that employs a front end filter with chip rate sam-pling. We will compare our equalization strategies with these two bounds. 19 3.1.1 Linear Equalization (LE) The L E employed for BPSK DS-UWB systems consists of a linear filter with coefficients f[k] optimized according to the MMSE criterion. Denoting filter coefficient vector by f = f[0] /[l] ... f[Nw-l] (3.1) and taking into account the AWGN, the optimized filer coefficients are given by [7] / = ( H H H + ^ I N J - 1 H f c 0 , (3.2) where H is given in (2.20), and 1^ is the (Nw x Nw) identity matrix. k0 denotes decision delay. Hfc0 is the fcoth column of H . The output d[k] of the MMSE linear filter is given by d[k] = fr. (3.3) Since the modulation scheme considered here is BPSK, the data estimate a[k-k0] can be obtained simply by considering the sign of the real part of the L E output d[k], i.e., a[k - k0] = sign{Re{d[fc]}}, (3.4) 3.1.2 Decision Feedback Equalization (DFE) The D F E equalizer consists of a feedforward filter (FFF) and a feedback filter (FBF). The received signal within the processing window is fed to the F F F . The F B F eliminates the post-cursor interference, i.e., the interference caused by previous data bits. The filters are jointly optimized according to the MMSE criterion [29]. The F F F coefficients /i?[fc] and the F B F coefficients fs[k] for MMSE D F E are given by fF[k] = ( H H " - H g f l H f s + ollNwy'Kk0, (3.5) SB = H ^ B / F , (3.6) 20 where qs is the number of previous interference symbols, and H i : g s is a matrix that contains the first qB columns of H . The parameter ko is again decision delay which can be optimized ([30]). Defining aB as the q& dimensional feed-back signal vector The output of the F B F is a weighted sum of the past decisions dB and the FBF coefficients fB, which results in elimination of interference caused by previous bits (assuming that all the past decisions were correct). 3.1.3 Widely Linear Counterparts For BPSK signaling over complex-valued channels, widely linear (WL) process-ing, i.e., joint processing of received signal and its complex-conjugated version should be considered [31]. W L equalization strategies for frequency-selective channels have recently been proposed in [32]. In particular, M M S E - W L E and M M S E - W L D F E strategies have been developed as extension to conventional MMSE-LE and MMSE-DFE, respectively. We present in the following the WL processing based equalization strategies for DS-UWB systems. We define the transformation as = a[k — k0 — 1] a[k — k0 — 2] ... a[k — k0 — qs] (3.7) the estimated data a[fc — ko] can be expressed as a[k - k0] = sign{Re{/Fr - fB dB}}, (3.8) X^X:X = [XTXH)T. (3.9) Widely Linear Equalization (WLE) The W L - M M S E filter minimizes the mean-squared error J •WL E{ReMk-k0}-(fWL)H*}2} E{\\a[k-k0]-(fL)Hr\\2l (3.10) and it is given as [32] (3.11) 21 and the corresponding estimated data &[k — ko] can be expressed as a[k - ko] = sign{(/^)Hr}. (3.12) For a computational complexity comparison, we note that the computation of the L E (3.2) involves the inversion of an Nw x Nw matrix. The W L filters entail the inversion of a 2NW x 2NW matrix. Since the matrix inversion is only done once, it does not count towards complexity. Therefore, the increase in computational complexity is fairly moderate. Widely Linear Decision Feedback Equalization (WLDFE) For MMSE-WLDFE, in addition to W L processing of the received signal vector r, feedback filtering is applied. The W L D F E output is a real-valued number which can be expressed as d[k]= fFr-fBkB, (3.13) where the F F F and the F B F are given by [32] SF — ( H H - H i : g B H 1 : g B +-^I2jO~ H F C O , (3T4) and fB = n"qBfF, (3.15) The feedback signal vector a# is defined in (3.7), and H g B is a matrix that contains the first qB columns of H . The estimated data a[fc — ko] can be expressed as a[k - ko] = sign{d[A;]}. (3.16) It should be noticed that the FBFs used in W L D F E are real-valued, which yields a small complexity advantage of W L processing over conventional linear equalization. Again, the matrix inversion is only done once, so it does not count towards complexity. The derivations of the signal-to-interference-plus-noise ratios (SINRs) of the equalization schemes discussed above are shown in Appendix A. 22 3.2 Finger Selection Algorithms A chip-rate processing window with length longer than the overall channel im-pulse response is employed at the receiver for detection. Since a UWB signal has a very wide bandwidth, the number of resolvable multipath components is usually very large. Hence, it is not practical to capture all the multipath com-ponents. An implementation of multipath diversity combining can be obtained using a receiver which combines the M best out of Ltotai multipath components [33]. Those M best components are determined by a finger selection algorithm. The selective-RAKE has been employed in [10] to combine the dispersive paths in a UWB multipath environment. Post-RAKE equalization is necessary in order to effectively mitigate ISI caused by the frequency selective nature of the UWB channel. Since the R A K E receiver is optimal only under an addi-tive white Gaussian noise assumption, it will suffer considerable performance degradation when the signal is contaminated by intersymbol interference. As a result, the use of selective-RAKE receiver for multipath energy capture and combining is ineffective to combat the intersymbol interference, since the lo-cations that involve the maximal paths of desired symbol may also involve the paths of the other symbols with higher magnitudes, or having strong depen-dence with that of the desired symbol [34]. In contrast, an MMSE linear receiver takes into account the relative impor-tance of each interfering symbol and the background noise, and minimizes the mean-squared error between the output of the receiver with the desired sym-bols [7]. Therefore, it is reasonable to employ an MMSE receiver to capture multipath components. For an MMSE receiver, the "conventional" finger se-lection algorithm can be viewed as choosing the paths which will result in the highest SINR, For optimal selection of M non-uniformly spaced taps out of a total of Ltotai taps, an exhaustive search is needed and this requires the MMSE detection performance to be evaluated for (^ o t a l) possible combinations of tap subsets. 23 This is not feasible for UWB because of the large value of Ltotai. The finger selection problem can be viewed as forming a transmission matrix Us by selecting a subset of rows from the overall transmission matrix H of (2.19) such that the SINR of this subset of rows is maximum. Appendix A shows the SINRs derivation of various equalization schemes. From (A.6) of appendix A, we know tap selection is equivalent to choosing so as to maximize u, with and Hs,ko denotes the &oth column of matrix H5. In the following we consider two suboptimal algorithms for finger selection: Greedy Algorithm (GA) and Simulated Annealing (SA). 3.2.1 Greedy Algorithm The Greedy algorithm [35] (GA) is a practical method for finding a subopti-mal solution. GA starts from an optimal solution to some component or small part of the data structure, and it considers additional components of the data structure one by one. However, there is no guarantee that making locally op-timal improvements will yield the optimal global solution. Suppose that at the (n — l)th step, the selected transmission matrix with (n — 1) rows is denoted as H n _ i . An nth row is selected from the remaining unselected rows and added to H n _ i to form a new matrix H n with n rows such that « = H g f c 0 ( H 5 H f + - f I ) - 1 ! ^ , (3.17) un = H n ] f c o (H„H; •n,ko (3.18) is maximized. The computational cost of GA is as follows. At the nth step, each of the remaining (Ltotai — (n ~ 1)) r o w s has to be examined to the nth row. As a 24 result, (3.18) is performed (Ltotai — (n — 1)) times at the nth step. To choose M from Ltotai rows, the matrix is inverted L + (L - 1) + ... + ( L M - M + 1) = { 2 L " - + X2 ~ M ) M (3.19) times. The G A is always updated in the direction of improvements and hence is quickly trapped in a local optimum. Therefore, it is reasonable to consider an algorithm that has mechanisms to avoid early convergence to local optima. In the following section, we discuss the Simulated Annealing, an algorithm that has the ability to escape from early local optima. 3.2.2 Simulated Annealing The Simulating Annealing (SA) [14] can locate a good approximation to the global optimum of a given function in a large search space. SA is deduced from the physical annealing process of solid material in metallurgy, a technique in-volving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one. In simulated annealing, a solution vector s represents a system state and the value f(s) represents the energy of the system at that state. Based on the Metropolis criterion [36], the transition probabilities pt of the system moving from the current state s to another state s is as follows: ( 1 if 6 < 0; Pt = < ( e" 5/T if 5 > 0. where 5 = f(s) — f(s) and T is the global parameter called the temperature [15]. One essential requirement for the transition probability pt is that it must 25 be nonzero when 5 > 0, meaning that the system may move to the new state even when it is worse (has a higher energy) than the current one. It is this feature that prevents the method from becoming stuck in a local minimum a state less ideal than the global minimum, but deceptively attractive because it is more ideal than any immediate neighbor. At fixed T, the system is likely to approach thermal equilibrium where the probability of a state s is proportional to e~^s^T. If the system is cooled down sufficiently slow, the SA reaches the global minimum. The evolution of the state s depends crucially on the temperature T; therefore, the range of the temperature T and how it is cooled down are important factors in SA. We consider the following cooling schedules. • Geometric cooling: The temperature T is decreased after each iteration to aT. If the initial temperature is Tj, the final temperature is T/, and the number of iterations is / , then a — (Ty/Tj) 1/ 7. Experiments are required to decide a suitable range for the temperature. • Constant temperature: At too high temperature, the annealing process becomes complete random, whereas at too low temperature, the system will increasingly favor moves that go "downhill" (to lower energy values), and avoid those that go "uphill" [15]. In particular, when T becomes 0, the procedure will reduce to the greedy algorithm which makes the move if and only if it goes downhill. If the number of iterations / is limited, it may be advantageous to spend all the time at a fixed temperature in the middle. This temperature should allow the annealing process to escape from local optima and perform a thorough search in the regions near good solutions. Table (3.1) shows the pseudo-code implementation of the simulated annealing heuristic, as described above, starting from state SQ and continuing to a max-imum of Imax iterations. 26 Table 3.1: Pseudo-code for simulated annealing heuristic. 1 / / Simulated Annealing heuristics Select initial vector s, set best solution s = s for(i = l,...,Imax - 1) Select next trial vector s from s by cyclic bit-flipping Calculate 5 = f(s) — f(s) Generate a uniform random number r in (0,1) if (6 < 0 or r < e-5/T) s — s end if if (f(s) < /(«)) s = s end if Update T according to cooling schedule end for Return s 27 Table 3.2: Parameters for the considered BPSK DS-UWB systems. BPSK Spreading Codes [6] iV = 24: [-1,0,1,-1,-1,-1,1.1,0,1. 1,1,1,-1,1,-1,1,1,1,-1,1,-1,-1,1] TV = 6: [1,0,0,0,0,0] BPSK spreading Codes of Interferer [6] TV = 24: [-1,-1,-1,-1,1,-1,1,-1,1,-1, -1,1,-1,1,1,-1,-1,1,1,0,-1,0,1,1] N = 6: [0,0,0,1,0,0] Channel Models CM1 and CM4, lower band from 3.1 to 4.85 GHz Pulse Shape Square root-raised cosine (a=0.3) [6] Date rates 57 Mbps (iV=24) and 220 Mbps (iV=6) [6] The computational cost of SA is as follows. At each iteration, (Ltotai — (M — 1))M matrix inversions are performed. The total number of matrix inversions after / iterations is {Ltotai — (M — 1))MI. A simple way for finger selection is to choose the strongest paths (SP) from the channel impulse response. It is informative to determine the performance gains of the G A / S A relative to SP. Of course, these gains are achieved with a higher computational cost. 3.3 Simulation Results and Discussion In this section we provide simulation results for the different equalization and finger selection schemes. First, we describe the system parameter value used in the simulations. 3.3.1 Simulation Parameters We consider the lower UWB operating band from 3.1 to 4.85 GHz. The system parameter value used are shown in Table 3.2. For the results showing the per-formance of the various equalization and finger selection schemes, simulations 28 Linear MMSE (qp=4) MFB2 • - • - • M F B 1 IU 8 9 10 10log 1 0(E b/N 0) [dB] Figure 3.1: B E R versus 10iog 1 0(£ 6/iVo) for linear MMSE CM1 and N = 24. Also shown MFB1 and 2 [10]. are performed over 100 channel realizations of CM1 and CM4. The results show the performance averaged over the best 90 out of 100 channel realiza-tions [25]. For all results it is assumed that perfect channel state information is known by the receiver, and a favorable delay parameter k0 value is found by testing various value within a reasonable range [30]. The B E R results are plotted as function of 101og 1 0(E b/Ao), where Eb is the average received energy per data bit. 3.3.2 Simulation Results for Equalization Schemes The performance results for the proposed equalization schemes for DS-UWB systems using BPSK modulation are presented and compared with the matched filter bounds MFB1 and 2 developed in [10]. First, the B E R results for the 29 10 ' I 1 L I I I J I I [ : Linear MMSE(qF=15) •-: : : : : : : : : : ; : : : : : : : : : : : ; : : : : : : : : : : : ; LEDFE<q F =i5 ,q B =i i ) '•-4 5 6 7 8 9 10 11 12 13 14 10log 1 0(E b/N 0) [dB] Figure 3.2: B E R versus 101og1 0(£6/AT0) for linear MMSE and D F E CM4 and N = 24. Also shown MFB1 and 2 [10]. different equalization strategies without W L processing are presented. Subse-quently, the improvement due to W L processing are considered. Fig. 3.1 shows the B E R performance of the DS-UWB system for CM1 and spreading code length N = 24 as function of 101og10(£'()/A7o). The B E R curves of MFB1 and MFB2 are also plotted. The processing window has a length of Nw = N(qp + 1) with qp = 4. It is observed that a linear MMSE equalizer can achieve a performance very close to MFB2. At BER = 10~5, the linear MMSE equalizer is within 0.2 dB of MFB2. The B E R performance for D F E and W L processing for CM1 A=24 is very close to and can not be distinguished from that for linear MMSE, so they are not plotted in the figure. Only lit-tle performance gain can be achieved if other relatively sophisticated schemes are employed. Therefore, the simple linear MMSE equalization scheme can 30 4 6 8 10 12 14 16 10log 1 0(E b/N 0) [dB] Figure 3.3: B E R versus 10 log 1 0(£(,/A 0) for linear MMSE and D F E CM4 and N = 6. Also shown MFB1 and 2 [10]. provide a very good performance for DS-UWB detection for CM1 and A=24. This is due, mostly, to the relatively short delay spread for CM1 and the long spreading code applied. The curves for MFB1 and MFB2 are relatively close, and this shows that for BPSK DS-UWB systems, chip rate sampling does not result in significant performance degradation [10]. Fig. 3.2 shows the B E R curves for the DS-UWB system with the CM4 channel and N=24. For linear MMSE and linear DFE, qF = 15, and the number of previous symbols for D F E is = 11. It is observed that the B E R curves for L E and D F E are almost parallel to that of MFB2, and D F E is close to MFB2. L E and D F E show a similar performance, with a gap in power efficiency of approximate 0.15 dB. The gap between L E and D F E is slightly larger than 31 4 5 6 7 B 9 10 11 12 13 14 1 0 I ° 9 , 0 < E I , " V l d B l Figure 3.4: B E R versus 101og10(JE6/Wo) for Linear MMSE and W L MMSE CM4 and N = 24. Also shown MFB1 and 2 [10]. for CM1 and N=24. We can conclude that even for the worst channel (CM4), linear M M S E and D F E can still provide good performance for low data rate DS-UWB systems. As a third scenario, we consider the simulation results for spreading N=6 and CM4 channel in Fig. 3.3. For L E and DFE, qF = 50, and qB = 44 for DFE. L E still perform quite well for this worst case scenario as the B E R curves for L E is only 0.6 dB from MFB2. The gap in power efficiency between L E and the optimum case, MFB1, is about 1.0 dB. Also, we observe that D F E outperforms L E for the same selected filter order by approximately 0.4 dB. Compared to the low-rate case with N=24 in Fig. 3.1, much longer processing windows are needed for efficient equalization because ISI is more severe in N=24 than that in N=6. 32 4 6 8 10 12 14 16 1Dlog10(Eb/N0) [dB] Figure 3.5: B E R versus 101og 1 0(£ t/iVo) for linear MMSE and W L MMSE CM4 and N = 6. Also shown MFB1 and 2 [10]. Linear vs. WL Processing From Fig. 3.4, which corresponds to the low data rate (45 Mbps) scenario with Af=24, it can be seen that W L MMSE provides a performance gain of around 0.2 dB compared to LE . For the high data rate scenario corresponding to CM4 and N=6, the benefits of W L processing over linear processing are illustrated in Fig. 3.5, where the B E R curves for L E and D F E are compared with W L E and W L DFE. It can be observed that, for filters of the same order, W L processing outperforms linear processing for both M M S E and DFE. W L MMSE gains power efficiency of 0.4 dB over L E for low BERs, whereas the gains of W L DFE over linear D F E are in the order of 0.3 dB. It should be noted that W L MMSE achieves a performance very close to that of DFE, and is less complex than D F E because no decision feedback is required for W L MMSE. 33 Greedy algorithm, CM1, N=24 Greedy algorithm, CM4, N=24 Greedy algorithm, CM4. N=6 -6H 20 40 60 Number of taps SO 100 120 Figure 3.6: Average SINR loss as function of number of fingers for the three scenarios(CMl, N = 24), (CM4, N = 24) and (CM4, N = 6) at SNR=14dB. 3.3.3 Simulation Results for Finger Selection Schemes In this section, we present the simulation results for the finger selection schemes. First, we study the loss in average SINR for a finite number of fingers F < F^, where Foo denotes the number of all fingers within the processing window. Subsequently, the B E R results for the finger selection schemes are presented. Simulation Results for Greedy Algorithm Fig. 3.6 shows the average SINR loss as a function of number of selected fingers using the G A for the three scenarios (CM1, N = 24), (CM4, N = 24) and (CM4, N = 6) at SNR=14dB. The average SINR loss is defined as where SINR{F) and SINR^) denote the SINR with the F selected fingers 34 ASINR(F) = ^f^(10\og-10 SINR(F) SINR(F00) (3.20) .1 1 l I-.'..' l I t i: - - - GA + Linear MMSE, F=16 • - • - • GA + Linear MMSE, F=32 Linear MMSE, F 4 5 6 7 8 9 10 11 12 13 14 10log l 0(Bb/N0) [dB] Figure 3.7: B E R versus 101og 1 0(£ , 6/A f 0) using the GA for CM1, N = 24. and the SINR with all fingers, respectively. The number of channel realizations, Nr , is set to 100 in our simulations. We observe that for CM1, F=32 fingers incur only a very small SINR loss of 0.3 dB, and for CM1 a good capture of the useful received energy is accomplished with F > 16 fingers. In the case of CM4, on the other hand, non-negligible SINR loss occurs for small to moderately large number of fingers F < 50. This is due to the long delay spread associated with CM4. A rather large number of fingers F > 64 would be required to approach the optimum performance. Fig. 3.7 - 3.9 present the curves for the DS-UWB for finite number of fingers selected by the G A for three scenarios (CM1, N=24), (CM4, N=24) and (CM4, N=6), respectively. The length of the processing windows is the same as that was used in previous plots of corresponding scenario. In general, the B E R performance improves as the number of selected finger increases. For CM1, 35 6 8 10 12 14 16 18 10log l 0(E b/N 0) [dB] Figure 3.8: B E R versus 101og10(f76/^b) using the GA for CM4, N = 24. 32 fingers selected by the G A can approach within 0.2 dB of the optimum (all fingers), while more fingers are needed for CM4 to achieve good performance. For the same number of selected fingers, low data rate achieves a performance better than high data rate for CM4, with respect to the all fingers case. For example, for L E built from the selected 24 fingers in CM4 channels, the gap in power efficiency to all taps is 2.3 dB for N=24, and 3.2 dB for N=6. W L processing provides performance better than linear processing in all scenarios. A large gap in power efficiency is discovered for CM4 and N = 6, with this gap becoming narrower as more fingers are selected. We also consider the performance of the combination of equalization schemes and the GA. Fig. 3.10 shows the B E R curves as function of 10\ogw(Eb/N0) for the equalizers for CM4 N — 6. These equalizers are built from the fingers selected by the GA. It is observed that W L DFE significantly outperforms 36 4 6 8 10 12 14 16 18 10log,0(Eb/N0) [dB] Figure 3.9: B E R versus 101og10(£6/./Vo) using the G A for CM4, N — 6. L E for the same number of selected fingers, but the gap in power efficiency decreases as more fingers are chosen. For a fixed number of fingers, the perfor-mance for W L MMSE is very close to that of linear DFE. We further observe that the performance for W L DFE with 16 fingers approaches within 0.3 dB of that of L E with 24 fingers at low BER. Fig. 3.11 shows a B E R performance comparison between SP and GA for DS-UWB of CM4, N = 6. It is observed that the G A outperforms the SP for a fixed number of selected fingers, at the expense of additional computational cost. The GA algorithm has a performance significantly better than the SP for a small umber of fingers, but the gap in efficiency between the GA and the SP drops as more fingers are chosen because the GA and the SP might end up selecting same fingers if the number of fingers to be used for detection is large. This observation is supported by Fig. 3.12, which shows the SINR loss 37 BER performance of CM4 N=6 based on Greedy Algorithm - — r — • 1—• 1 r l O l o g ^ / t y IriB] Figure 3.10: B E R performance comparison for 4 equalization schemes with Greedy Algorithm (GA) for CM4, N=6. due to a finite number of selected fingers. A similar conclusion can be drawn for other scenarios (CM1, N = 6) and (CM4, N = 24). Simulation Results for Simulated Annealing By comparing the SINR obtained by the SA with an initial state, to the SINR of that initial state, we can determine the SINR gain of the SA. It is informa-tive to compare the performance between the SA and the GA. Fig. 3.13 shows the average SINR gain, which is obtained by comparing the SINR of the SA with different initial states to a common initial state obtained by SP, for various number of iterations as a function of search space for 100 channel realizations. The search space M is defined as the M strongest pathes. The number of selected fingers is fixed as 16. The initial state is obtained by 38 10log, 0(E b/N 0) [dB] Figure 3.11: B E R performance comparison between Strongest Paths (SP) method and Greedy Algorithm (GA) for CM4, N = 6. GA and SP, respectively. We found that both the geometry cooling and con-stant temperature cooling schedules achieve the same performance, so only the constant temperature cooling schedule results are shown here. It is observed that, regardless of initial state, for a large search space, SA converges in only a few iterations. For example, for search space of all taps, the SINR gain of SA over initial state by SP is very close to that of initial state by GA, after only 8 iterations. The SINR gain is found to increase as the search space expands, for a fixed number of iterations. For the initial state obtained by SP and search space of 32 taps, an SINR gain of 0.95 dB is achieved after only 4 iterations. If the search space is increased to the 48 strongest taps, the resulting SINR gain increases to 1.03 dB. However, if the search space is enlarged to all taps, only 39 0| -2 -3 1 /• * / t I J / i / ' / f / 1 / ' / ' / ' /...I / ' I 1 / ' / ' / ' l 1 / ' / 1 I ' I ' / 1 1 I 1 1 •'• • Greedy Algorithm — - — - Strongest Pathes method i i i 0 50 100 150 200 250 300 Number of fingers Figure 3.12: Average SINR loss as function of number of fingers for the SP and the G A for CM4, A' = 6. another 0.1 dB gain can be achieved, and this small gain comes at the expense of additional computations. Furthermore, a notable SINR improvement is achieved with SA compared to the SP method; on the other hand, no significant SINR improvement is found compared to the GA. More specifically, gains of up to 1.35 dB and 0.3 dB are achieved compared to the SP method and the GA, respectively. We also ob-serve that SA with search spaces of 100 strongest paths results in performance very close to that with full space search. Finally, it is observed that 8 iterations are adequate for SA because only little gain is obtained by performing more iterations. In general, GA is preferred for finger selection because it can achieve per-40 • Initial state obtained by GA, 16 iterations Initial state obtained by GA, 8 iterations Initial state obtained by GA, 4 iterations Initial state obtained by SP, 16 iterations 0 Initial state obtained by SP, 8 iterations - •©- - Initial state obtained by SP, 4 iterations * Gain of GA over SP, 0 Iteration 0 50 100 150 200 250 300 Search space (fingers) used by Simulated Annealing Figure 3.13: Average SINR gain as function of search space used by Simulated Annealing for selecting 16 fingers with initial state obtained by SP method, for CM4, N = 6 at SNR=14dB. formance very close to the optimum while incurring moderate computational complexity. We can also conclude that a search space of 64 is adequate to get a good performance since little gain is obtained if the number of taps increased. Comparison between the GA and the RAKE combining followed by equalization from [13] It is proposed in [13] that equalization be employed at the output of the R A K E combiner to mitigate ISI is . The structure of these receivers is simple because equalization is processed at the symbol level. In this section, we compare the performance and complexity of the receiver between the receiver in [13] and GA. For a fair comparison, we use the same set of channel realizations in both cases. 41 Figure 3.14: B E R versus 10 log10(jEVJV0) of the G A and R A K E combining [13] for CM4, N = 24. Fig. 3.14 and 3.15 shows the BER versus 10logw(Eb/NQ) of the G A and R A K E combiner [13] for CM4, AT = 24 and CM4, N = 6, respectively. A R A K E com-biner with 16 fingers is employed to capture multipath components. We can observe that, for CM4 and N = 24, the R A K E combiner followed by linear MMSE equalization results in a gain of 0.6 dB over the G A with 16 fingers, and 0.8 dB for the widely linear MMSE equalization scheme. For CM4 and N = 6, these gains are 1.1 dB and 1.0 dB, respectively. It seems that R A K E combiner followed by a equalizer can result in performance gain over the GA, however, we need to compare the complexity of these two algorithms before making any conclusions. At the R A K E combiner, in our comparison, each of the employed 16 fingers 42 Figure 3.15: B E R versus 10logw(Eb/N0) of the GA and R A K E combining [13] for CM4, N = 6. has to sample N consecutive received chip-rate signals. Equalization schemes are processed at the symbol rate at the output of the R A K E combiner. The computational cost of the equalization is dominated by the matrix inversion to decide the filter coefficients for LE . The matrix inversion is done once, and the cost is 0((Lchannei + l ) 3 ) , with Lchananei denotes the length of overall chip rate IR. At least (16 + 24 — 1 = 39) signals are sampled at R A K E to detect one bit (in the extreme case, 16 x 24 = 384 signals are needed), and this will result in high complexity for hardware implementation. While for the GA, each of the employed 16 fingers needs to capture one chip-rate signal, and the equalization schemes are also processed at chip rate. 16 received signals are used for symbol detections. The overall computational cost is mostly caused by the matrix inversion, which is 0(163). Therefore, the 43 overall computational cost of R A K E combiner followed by equalizer is higher than that of the GA. In terms of hardware implementation, R A K E combiner followed by equalizer is more complex than the GA. By comparing Fig. 3.8 and Fig. 3.14, we observe that the G A with 20 fingers achieves performance slightly better than that of R A K E combiner with 16 fingers followed by an equalizer. We conclude that the GA is preferred over the R A K E combiner for implementation due to its simple structure and low complexity. 44 Chapter 4 Channel Estimation for a Single In a UWB system, an MMSE receiver (or other receivers discussed in Chap-ter 3) is typically employed to detect information symbols. To fully capture the signal energy spread over multiple paths, channel parameters values are necessary to construct an MMSE receiver. However,channel information is not known a priori. Recently, maximum-likelihood (ML) channel estimation methods have been proposed in [37], which provide a theoretical guidance for evaluation of other channel estimators. However, ML-based channel estima-tion methods are computationally complex. In this chapter, we will investigate several low-complexity channel estimation schemes for the DS-UWB systems. A DS-UWB system with a single user was considered in the previous chapter. We also consider in this chapter channel estimations for a single user. We study various schemes for channel estimation, depending on the availability of training sequences. In this section, we consider the problem of estimating the physical channel of a given user from the received signal, based on the knowledge of the spreading DS-UWB 4.1 Blind Channel Estimation 45 code for that user. The transmission model used here is the one described in Chapter 2. In practical applications, the spreading code of the desired user is usually known to the receiver. The equivalent overall spreading sequence for the user is h = Cg (4.1) where C is the (N + Lf) x (L/ +1) spreading matrix formed from the spreading code of the user, g is the UWB channel vector, and Lf is the order of the channel. c[N-l] 0 ... 0 c[N - 2] c[N - 1] C = . c[N-2] ... . (4.2) 0 0 c[l] c[0] g = g[o] (4.3) [g[Lf] g[qf-l] Assume a symbol with decision delay ko unit is desired. Recall from (2.19)that the effective spreading sequence for the desired symbol is the k0th column of H, denoted as Hfc0 which can be expressed as H f c 0 = Cg (4.4) where 0 C 0 (4.5) is an N(qf + 1) x (qj + 1) matrix and <?/ is as defined in (2.17). Let C r denote the covariance matrix of the received signal vector. From (2.20), we have C r = HH" + a2nl. (4.6) Assume that H has full column rank [i.e., rank(H) = (qf+L+1), where L is defined in (2.15)]. Let Aj > A 2 > • • • > Ajv( g / + 1) be the eigenvalues of 46 Cr. Since the matrix H has full column rank, the signal component of the covariance matrix C r (i.e., HH H ) has rank (qf+L+1). Therefore, we have [16] A; > for i = 1,..., qf+L+1, Xi = ol for i = qf+L+2,..., N(qf+1), Because the ambient channel noise is white, by performing an eigendecompo-sition of the matrix C r , we can obtain [16] C r = U 8 A s U ? + <#J n U? (4.7) where A s = diag(Ai,...,Ajv(9/+i)) contains the (qf+L+1) largest eigenvalues of C r in descending order, U s = [u\- • -uqf+L+i] contains the corresponding or-thogonal eigenvectors, and U n = [uqf+i+2- • •ix./v(g/+i)] contains the (N(qf+1)-(qf+L+1)) orthogonal eigenvectors that correspond to the eigenvalues o\. The column space Us is called the signal subspace and its orthogonal complement, the noise subspace, is spanned by the columns of U n . The focus in this section is on the performance analysis of the subspace-based blind detection in a multipath environment, assuming the signal subspace com-ponents are known. If a training sequence is not available, the multipath channel g can be estimated blindly by exploiting the orthogonality between the signal and noise subspaces. Specifically, since U n is orthogonal to the column space of H, and Hfc0 is in the column space of H, we have U ^ H f c o = U ^ C g = 0. (4.8) Some constraint on g needs to be imposed in order to avoid the trivial solution g = 0. In particular, it is desirable to constrain the energy of the user of interest to a constant. It is proposed in [38] that, g, an estimate of the channel response g can be obtained by computing the minimum eigenvector of the matrix ( C T U n U ^ C ) . The resulting linear MMSE detector is determined by / = U ^ U f C g . (4.9) 47 Note that the estimated channel response is constrained to have unit norm, but this constraint will not affect the result of symbol detection because the output of the detector is different only by a real (nonzero) multiplicative term. 4.2 Training-Based Channel Estimation In this section, we investigate the estimation of the UWB channels with train-ing sequences. Commonly used channel estimation techniques are the least squares (LS) [39] and maximum likelihood (ML) estimation. Because the UWB channel delay spread is very large, the application of these methods is computationally complex and is not practical. We need to find a compu-tationally simple algorithm that can achieve good performance. A matching pursuit (MP) algorithm [41] is investigated in [42] for estimation of the sparse channels. In [18], an MP followed by cancelation (MPC) algorithm is investi-gated to estimate C D M A channels with large delay spreads. Performing better than LS algorithm, M P C algorithm is discovered to have significantly low com-plexity compared with LS algorithm. Since the application of the M P C on the DS-UWB has not been previously studied, we will investigate the performance of this algorithm for the DS-UWB and the resulting complexity. The UWB systems are utilized for short-range high data rate transmission, and the channels stay unchanged duration the transmission a data packets. We fo-cus only on time-invariant channels.The M P C algorithm is now discussed. Starting from the UWB system model (2.20) for a single user, an alternative representation of the signal model as r = Th + n, (4.10) where r and n are as defined in (2.20), and h denotes the chip-rate generalized UWB channel impulse response. T is a Toeplitz matrix consisting of chip-rate 48 sampling training symbols t[n] 0 ... 0 t[n-l] 0 0 t[n] 0 ... 0 t[n - 1] 0 0 . ... 0 0 ... 0 t[n + l] 0 ... 0 t[n] 0 0 t[n + l] 0 ... 0 t[n] t[n + N t r a i n i n g - 1] 0 ... 0 t[n + Ntraining - 2] 0 T = (4 11) where Ntraining denotes the length of training symbols and T is of dimension NNtraining x (L/ +1)- N is the spreading factor, and Lf is the order of the chip rate channel impulse response. The problem now is to approximate the vector r in terms of a linear combination of columns from the matrix T, i.e., from (4.10), we must find h such that Th « r. The M P C algorithm described next gives an efficient method for obtaining a suboptimal solution to this problem. The M P C algorithm consists of two steps: (1) The matching pursuit (MP) step and (2) the cancellation (C) step. • The matching pursuit (MP) step: The MP step approximates the value of each channel coefficient. We first find the column in the matrix T = [t1? t2, ...,tjr,/+1], which is best aligned with the signal vector r 0 = r and this is denoted [41]. Then the projection of r along this direction is removed from r 0 and the residual r i is obtained. Now the next column from T, tfc2, which is best aligned with r i and a new residual, r2, is found. The algorithm proceeds by sequentially choosing the column which best matches the residual until the number of channel coefficients has been se-lected (we assume the number of channel coefficients is known, however, the value of each coefficient needs to be determined). The pth iteration is described in the follows. 49 The vector from T most closely aligned with the residual r p _i is chosen, where the alignment is measured as the projection of the residual onto the vector, i.e., I t^r _ i I2 kp = arg max (4.12) ' I  w lr The new residual vector is then computed as (tgrp_i)tfc rkp = rkp-i j|-7—p— (4.13) and the channel coefficient at position kp is hkp — (tj^rp_i)/ || tkp || 2. The iteration is repeated until the number of coefficients has been selected. • The cancelation (C) step: The performance of MP deteriorates signif-icantly due to column correlations in the matrix T [43]. To overcome this performance degradation, the cancelation step uses the already estimated channel coefficients to remove interference from the received vector in or-der to identify the channel coefficients more accurately. The interference cancelation is as follows. Lf+l £fcp = t £ ( r - £ tkphki)/ || tfcp || 2 . (4.14) The updating is stopped when the change in the coefficients falls below a certain threshold, but it is observed in our simulation results that the cancelation step needs to be performed only once to achieve good performance. 4.3 Complexity Comparison between the MPC and other Channel Estimation Algorithms In this section, we compare the computational complexity of the M P C al-gorithm with other channel estimation algorithms. Commonly used channel estimation techniques include the LS and the M L estimation. Since the com-plexity of the M L is higher than that of the LS, we will compare here the 50 Table 4.1: Complexity comparison for channel estimation algorithms. M P C 0(2(L, + 1)) LS 0((Lf + l ) 3 + (L; + l)NNtraining + (Lf + l)NNtraining) complexity of the M P C and the LS. Table 4.1 shows complexity comparison for channel estimation algorithm. LS based estimations [46] can be obtained as h = (T T T)- 1 T T r (4.15) The complexity of LS is dominated by inversion of an ((L/+1) x(L/+l ) ) matrix (TTT), and it is not practical for long spread delays UWB channels. The complexity of M P C mainly comes from the M P step, and the computational cost of this step is the sum of (4.12) (0(Lf + 1)) and (4.13) (0(Lf + 1)). The comparison clearly shows the complexity of the M P C is much lower than that of the LS algorithm. 4.4 Results and Discussions In this section, simulation results for the blind channel estimation and channel estimation with training sequences for the BPSK DS-UWB systems are pre-sented. In Section 4.3.1, we present results for the blind channel estimation. The results for channel the estimation with training sequences are presented in Section 4.3.2. For all simulations, qf = 15 is for (CM4, N = 24) and qf = 50 for (CM4, N = 6). 4.4 .1 Simulation Results for the Blind Channel Estima-tion Fig. 4.1 shows the B E R performance of the DS-UWB system with N = 24 and CM4 as function of 101og10(£^f,/A/o). The simulation shows the performance of the subspace-based blind detection in multipath, assuming the signal subspace components U s of (4.7) are perfectly known. This is a lower performance 51 0 Blind Linear MMSE equalizer ; Exact Linear MMSE equalizer ... 10lo» 1 0 (E l /N 0 ) [dB] Figure 4.1: B E R versus 101og10(E,6/A''o) for Blind Channel Estimation for CM4 and N=24. bound for the subspace-based blind channel estimation, because in practical applications, perfect knowledge of C r is not known at the receiver. An L E blind detector with (N + Lf) taps is built from the estimated channel. No finger selection schemes are performed in this simulation since all taps are used. We compare the performance of the blind detector with the performance of the all-tap L E assuming perfect channel information. It is observed that the blind L E suffers a performance loss of approximate 8 dB -compared to the exact L E for at a B E R of 10 - 3 . Therefore, the blind channel estimation cannot produce a good performance for the DS-UWB systems. This result is consistent with the result shown in figure 2.14 of [40]. We can conclude that the blind channel estimation methods are not suitable for the DS-UWB due to the long delay spreads of the UWB channels. 52 BER performance of UWB CM4 N=24 applvng MPC algorithm using 100 training bits and two-stage adaptive filter —fa— MMSE equalizer based on MPC algorithm with 100 training symbols ; -- 8 — MMSE equalizer based on MPC algorithm with 150 training symbol! .. . • " D " MMSE equalizer based on MPC algorithm with 200 training symbol! • -Exact linear MMSE equalizer 10log t 0(Eb/N0) |dB] Figure 4.2: B E R versus 10log10(Eb/N0) for channel estimation with training symbols of different length for CM4 and N=24. 4.4 .2 Simulation Results for Channel Estimation with Training Sequences Fig. 4.2 shows the B E R performance of the DS-UWB systems with N = 24 and CM4 as function of 101og10(£b/./Vo), and the B E R performance assuming exact channel information is available. The receiver first estimates the UWB channel using the M P C algorithm with training sequences, an L E is then built from the estimated channel. We assume the UWB channels are time-invariant during the channel estimation and the data transmission. We compare the B E R performance of the M P C algorithm with training se-quences of 100, 150, and 200 symbols, respectively. As expected, the B E R performance improves as the length of training sequence increases. At the B E R of 10 - 5 , the M P C algorithm a training sequence of 200 symbols achieves 53 Figure 4.3: B E R versus 10\og10(Eb/N0) for channel estimation with training symbols of different length for CM4 and A=6. a performance gain of 0.6 dB over that with a training sequence of 100 sym-bols. We further observe that the M P C algorithm with 200 training symbols suffers a performance loss by approximate 1 dB compared to L E with exact channel information. Fig. 4.3 shows the B E R performance of the DS-UWB system for N = 6 and CM4 as function of 10\ogw(Eb/N0), and the B E R performance assuming exact channel information is available. At a B E R of 10 - 5 , the M P C algorithm with 500 training symbols achieves a performance gain of 1.2 dB over that with 200 training symbols. It is observed that the M P C algorithm with 500 training symbols suffers a performance loss by approximate 0.6 dB compared to the L E with exact channel information. 54 SINR of UWB CM4 N=24 applying MPC algorithm at SNR = 14dB 15 r 1 i 1 1 1 1 1 r 8I i I I I l I I l 1 20 40 60 80 100 120 140 160 180 200 Number of training symbols Figure 4.4: SINR of M P C algorithm versus number of training symbols of different length for CM4 and iV=24 at SNR = 14dB. The results in Figs. 4.2 and 4.3 indicate that the channel estimation by the M P C algorithm with a training sequence is suitable for the DS-UWB systems because with only a few hundreds training symbols, the performance is rela-tively good. We also investigate the SINR performance of the M P C algorithm with a train-ing sequence. Fig. 4.4 shows, at SNR = 14 dB, the SINR obtained by the M P C algorithm with different number of training symbols for A=24 and CM4. As expected, the SINR improves as number of training symbols increases. The SINR improves rapidly with increasing training symbols when the number of training symbols is less than 80, but the SINR improvement is small as more training symbols are transmitted; for example, difference of only 0.5 dB is ob-served between training sequences of 200 symbols and 100 symbols. We can 55 20 40 60 80 100 120 140 160 180 200 Number of training bits Figure 4.5: Channel estimation error of M P C algorithm versus number of training symbols of different length for CM4 and JV=24 at SNR = 14dB. conclude that, for (N=2A and CM4), 200 training symbols are adequate for the channel estimation with the M P C algorithm. This conclusion is further supported by the simulation results shown in Fig. 4.5. Fig. 4.5 shows the channel estimation error versus number of training symbols for N=24 and CM4, at SNR = 14dB. qf = 15. The channel estimation error is defined as the Euclidean distance between the estimated channel and the exact channel averaged over the number of channel coefficients [18]. Assuming h is the estimated of exact channel h, the Euclidean distance de can be expressed as dE =|| h - h || 2 . (4.16) Recall that we assume the number of channel coefficients is known. The chan-nel estimation error is observed to decrease as the number of training symbols 56 Figure 4.6: SINR of M P C algorithm versus number of training symbols of different length for CM4 and N = 6 at SNR = 14dB. increases, but after the number of training symbols reach a certain value (i.e., 80), the channel estimation error does not improve much even if more training symbols are used. Fig. 4.6 shows the SINR versus the number of training symbols for N=6 and CM4, at SNR = 14 dB. It is observed that the SINR at the output of the L E from the estimated channel improves as more training symbols are used for channel estimation. The channel estimation error curve for CM4 and N = 6 is shown in Fig. 4.7, and it is observed to undergo small changes when the number of training symbols exceeds 300. In practical applications, it is desired to select a limited number of taps for symbol detection, based on the estimated channels, for the sake of simple 57 t i i i r 1 0- ' l i i : i I i 1 i i 1 50 100 150 200 250 300 350 400 450 500 Number of training symbols Figure 4.7: Channel estimation error of the M P C algorithm versus number of training symbols of different length for CM4 and N = 6 at SNR = 14dB. hardware implementation. Therefore, the performance of the combination of channel estimation schemes and finger selection schemes is desired. Fig. 4.8 presents the B E R performance versus 10\og10(Eb/N0) for channel estimation with the M P C algorithm with 100 training symbols for CM4 and iV = 24. Different number of fingers are selected with the GA, and an L E equalizer is built correspondingly. Parameters for L E are identical to those used in chapter 3. It can be observed that the B E R performance improves as the number of selected fingers increases. The L E with 48 fingers by the G A approaches the L E with all taps within 0.6 dB. Fig. 4.9 presents B E R versus 101og 1 0(£ ,t/A 0) for channel estimation with the M P C algorithm with 200 training symbols for CM4 and N = 6. Different number of fingers are selected with the GA, and an L E is built. It can be 58 T Figure 4.8: B E R versus 10\ogw(Eb/N0) for channel estimation with the M P C algorithm with 100 training symbols, finger selection by the GA, for CM4 and N = 24. observed that the B E R performance improves as the number of selected fingers increases. The L E with 48 fingers chosen by the GA is within 0.8 dB of the L E with all fingers. Training symbol length on the order of hundreds can provide an acceptable channel estimate for the DS-UWB systems. Because DS-UWB systems oper-ate at very high data rates, the transmission of the overhead is small. We also investigate the performance of the different combinations of channel estimation schemes and other equalization strategies. Fig. 4.10 shows the performance comparison between L E and W L E for CM4 and N — 24. The channels are first estimated with the M P C algorithm with 100 training sym-bols, and 16 fingers are selected with the GA from the estimated channel. 59 A 6 8 10 12 14 16 18 IOIob^ Ej/N, IdSJ Figure 4.9: B E R versus 101og10(Eb/A70) for channel estimation with the M P C algorithm with 200 training symbols, finger selection by the GA, for CM4 and N = 6. Finally, L E / W L E is built for symbol detections. The B E R performance of L E and W L E with exact channel information are also shown. W L E is found to achieve a small performance gain of approximate by 0.2 dB over L E at B E R of 10~5. A performance loss by approximate 1.0 dB is observed between the L E with M P C algorithm and that with exact channel information. As for CM4 and N = 6The performance gap between L E and W L E is observed to be about 0.5 dB at low SNR, as from Fig. 4.11. The channels are first estimated with the M P C algorithm with 200 training symbols, and 16 fingers are selected by the G A from the estimated channel. Finally, L E / W L E is built for symbol detections. The 16-finger L E from the estimated channels suffers a performance loss of about 2.0 dB to that with exact channel information. 60 1 1 T 1 I I Figure 4.10: B E R versus 101og10(£ ,fc/A /0) comparison for channel estimation with the M P C algorithm with 100 training symbols for CM4 and N = 24, comparison is made between L E and W L E , finger selection with the GA. Also shown: B E R performance of L E and W L E of exact channels. 61 Figure 4.11: B E R versus 101og10(i?(,/iVo) comparison for channel estimation with the M P C algorithm with 200 training symbols for CM4 and N = 6, comparison is made between L E and W L E , finger selection with the GA. Also shown: B E R performance of L E and W L E of exact channels. 62 Chapter 5 Interference Suppression We have investigated various equalization schemes for single-user DS-UWB systems in Chapter 3, assuming no other interferences. But in practical ap-plications, UWB systems operate as multiple-access systems, in which mul-tiple users share the same radio resources. Similar to CDMA, a DS-UWB system assigns channels in a way that allows all users to use all frequency resources simultaneously, through the assignment of a spreading code to each user. A DS-UWB user of interest is therefore interfered with by other possi-ble DS-UWB users in the same network, and this kind of interference is called Multiple-access Interference(MAI). Also, a DS-UWB user might suffer from in-terference arising from other devices operating in the same band, such as IEEE 802.11a that operats in the same 5.0 GHz band. Interference mitigation is a major factor in the design of DS-UWB receivers. In this chapter, we discuss al-gorithms used for joint equalization and interference suppression for DS-UWB. It is well known that multiuser detection [7] can achieve good performance in multiple access systems. In addition, the coefficients of the receiver filters can be conventionally adapted to the channel and interference situation by using data-aided [19], [44] or blind [7], [45] adaptive algorithms. In practical UWB applications, it is reasonable to assume the receivers are decentralized receivers, i.e., the receivers exploit the knowledge of the spreading code and propagation channel of the user of interest only. In this chapter, we are concerned with 63 decentralized adaptive receivers, i.e., receivers formed by the concatenation of an adaptive filter with a suitable detection operation acting on the filter output. Data-aided recursive least square (RLS) and least mean square (LMS) algo-rithms have been investigated in [46]. The rate of convergence of the RLS algorithm is typically an order of magnitude faster than that of the LMS algo-rithm, at the expense of more computational cost. This is because the step-size parameter in the LMS algorithm is replaced by the inverse of the correlation matrix of the input vector [46]. The computational cost of RLS algorithm is impractical in UWB channels with large delay spreads. For this reason, this chapter focuses on the interference suppression with the LMS algorithm. Fur-thermore, it has been shown that under certain conditions, the performance of linear receivers can be significantly improved if not only the received signal, but also its complex conjugate, is precessed [7], [45] - [49]. It is shown in [21] that W L algorithms require a slightly lower computational complexity than their linear counterparts. In the next section, we briefly talk about the widely linear LMS (WL-LMS) algorithm and the widely linear minimum output energy (WL-MOE) algo-rithm. We assume that the CSI of the desired user is known at the receiver. The desired user is interfered with by other unknown asynchronous DS-UWB users (for MAI suppression) or NBI (for NBI suppression). The WL-LMS (WL-MOE) algorithm starts from the filter that is built with linear MMSE equalization scheme (3.2) based on the CSI of the desired user. 5.1 WL-LMS Algorithm The WL-LMS algorithm can be applied to recursively update the MMSE filter if the desired user transmits a training sequence or if reliable decisions on the desired user's transmitted data symbols are available. 64 The WL-LMS algorithm minimizes the instantaneous squared error signal e^sik] = t[k] - Re{^s[k]Hr[k]} ( 5 . 1 } where t[k] denotes the training symbol at time index k. f^Msik] a n d r[^] a r e the adaptive filter and the received signal vector at time k, respectively. The WL-LMS update equation is [21] i^Msik + 1] = & W + l*Y£8[k]T[k] (5.2) where is the step size. The only difference between the linear LMS algo-rithm [46] and the WL-LMS algorithm is the different definition of the error signal. For the LMS algorithm, eLMS{k] = t[k] - fLMs[k]"r[k]. The WL-LMS algorithm is obtained from the linear LMS algorithm simply by replacing the LMS error signal by its real part. Hence, the computational complexity of the WL-LMS is slightly lower than that of the conventional LMS algorithm [21]. The convergence and SINR analysis for the WL-LMS algorithm is shown in [21]. The steady-state SINR of the WL-LMS algorithm is found to be 1 T HLMS + SINRivt where SINRivt denotes the SINR of the widely linear MMSE receiver from equation (5) of [21]. For small step size ji where EK is the signal energy of «th user and E\ the energy of desired user. LT0W x K is the dimension of transmission matrix defined similarly to that of (2.19). 5.2 WL-MOE Algorithm The adaptive filter can be updated blindly using the W L M O E criterion if no training sequence is available. The only requirement for the W L - M O E algo-rithm is the knowledge of the desired user's spreading sequence. 65 The derivation of the W L - M O E algorithm can be found in [21]. The canonical representation for the W L - M O E filter is introduced as [21] ^Most^] — P i + X M O E [ ^ ] (5-5) where f^o£[fc] denotes the updated W L - M O E filter at time index k, and p x denotes the desired user's spreading sequence. x^ost^] is the component orthogonal to the desired user's spreading sequence, and it fulfills the following equation [21] < Pi,<oE[k] >WL= R e { p f x ^ [ A ; ] } = 0. (5.6) At each updating iteration, xj^^f/c], the component orthogonal to the desired user's spreading sequence, needs to be determined such that the variance of the output energy M O E H / L = R e l f ^ ^ / c ^ r ^ ] } is minimized. The widely lin-ear minimum-output-energy (WL-MOE) algorithm is obtained using gradient descent algorithm and is given by [21] <oE{k + 1] = AoE[k] ~ » • Re{z[k]}(r[k] - Be{zMF[k]}Pl). (5.7) where /j, is the step size. ZMF[&] — PiMfc] denotes the conventional matched filter output and z[k] = {mZbE[k\)"Y[k}- A comparison with [[7], Eq.(6.103)] reveals that the W L - M O E algorithm can be obtained from the linear M O E algorithm by simply replacing ZMF[k) and z[k] by their real parts only. This shows that the W L - M O E algorithm has a slightly lower complexity than its linear counterpart. The convergence and SINR analysis for W L - M O E algorithm can be referred to [21]. The steady-state SINR of the W L - M O E algorithm is [21] o t m r W _ SINRyr/^ S R m O E ~ 1 + V%8E + feSINR^, ( 5 ' 8 ) where i=K riZLOE = ^ ( 1 - Pi c o s 2 ( O k + ^ ) ) + (Lrow - l)al) (5.9) K=l with definitions pK = | q f q j and tpK = arg{qf qK} (| • | and arg{-} denote the magnitude and the phase of a complex number, respectively). q K is the normalized of p K , i.e., | q^q j = 1. 66 5.3 Two-stage Adaptive Filter The steady-state SINR of a data-aided adaptive algorithm is generally higher than that of a blind adaptive algorithm; however, the blind adaptive algorithm achieves a significantly higher speed of convergence [21]. Several methods have been proposed to improve the poor steady-state performance of blind adaptive algorithm. A dual-mode adaptive filter is proposed in [21] to improve the convergence speed of data-aided adaptive algorithm. The dual-mode adaptive filters starts with the blind adaption, and it switches to the decision-driven adaption as soon as the output SINR is sufficiently good for making reliable symbol-by-symbol decisions. Under standard convergence assumptions, the steady-state perfor-mance of the dual-mode filter is the same as the decision-driven receiver with initial training. Switching between nondata-aided and data-aided adaption modes, this dual-mode receiver with a single adaptive filter has the disadvan-tage that after mode switching, the resulting SINR may not be better, but could be worse than the SINR before switching [22]. In [22], a new class of blind adaptive receivers consisting of the serial concate-nation of two adaptive stages is proposed. The first stage is based on any blind adaptive algorithms, and the second stage is based on data-aided adaptive al-gorithms with the outputs of the first stage as training symbols. Based on this two-stage adaptive filter structure, we propose a two-stage wide linear adaptive filter with structure shown in Fig. 5.1. Our proposed two-stage receiver is formed by the serial concatenation of two adaptive stages. The first stage filter, m^Q^ffc], adapts according to the W L - M O E adaptive algorithm. The second stage filter, m^ 5 [ fc] , is based on the WL-LMS adaptive algorithm. The output at the decision device of the first stage follows the simple suboptimal symbol-by-symbol threshold detection rule: Mfc] = Re{Zl[k}} = Re{(m^[fc]) H r[fc]}. (5.10) 67 rfkl W L - M O E .^3aptiy|eJEilter WL-LMS . &y aptiy etE jltef ;zi[k] Z2M Mky Figure 5.1: Structure of two-stage filter. This output is fed into the second stage, which also receives the signal vector r[k] and adapts with t>i[fc] as training symbol. The output at the decision device of the second stage also follows the detection rule: b2[fc] = Re{z2[k}} = Re{(m^s[k])Hv[k]}. (5.11) Since the outputs of both stages of the two-stage receiver are always available, their SINRs are easily measured and the better one can be selected. While for a dual-mode receiver with a single adaptive filter switching between adaption modes, the output SINR must be compared with an empirical threshold in order to determine which adaption mode is to be used. A bad choice of this threshold could make the dual-mode receiver work in the wrong adaption mode most of the time [22]. The advantage of the two-stage receiver is obtained at the cost of an increased computational complexity because two adaptive algorithms must be run in parallel. 5.4 Narrow Band Interference DS-UWB systems unavoidably suffer from NBI (this kind of interference is called narrow band because its bandwidth is relatively small compared to UWB systems, but they usually transmit at much higher PSD), because they operate 68 ISM Band P C S IEEE 802.11b IEEE 602.11a 1.6 1.9 2.4 3.1 4 5 10.6 Frequency (GHz) Figure 5.2: Spectrum crossover of the NBI in UWB systems. in the same frequency band as UWB systems. This narrowband interference can sometimes be so serious that the UWB communication is totally prevented. Therefore, NBI suppression is of primary importance for UWB systems [50]. When dealing with NBI in UWB systems, it should be considered that there are some potential interferers with predetermined center frequencies and band-widths. The most serious interferer among all the potential interferers is the IEEE 802.11a W L A N (see Fig. 5.2). In this section, we will focus on IEEE 802.11a W L A N suppression in UWB communications. The IEEE 802.11a W L A N system uses 52 sub-carrier orthogonal frequency division multiplexing (OFDM). This system has a fixed bandwidth of 20 MHz. The operating bands of IEEE 802.11a are three 100 MHz wide frequency bands: 5.15-5.25, 5.25-5.35, and 5.725-5.825 GHz. Based on modeling an NBI as a single carrier BPSK modulated waveform, different types of NBI suppression have been studied for UWB systems [24] and [51]. A maximum ratio com-bining (MRC) rake receiver is employed in [51] to suppress NBI for DS-UWB systems by considering NBI as a sinusoidal tone. With the bandwidth as large as hundreds of MHz, IEEE 802.11a interference can not be modeled as a BPSK modulated signal or as a sinusoidal tone any more. Hence, many proposed methods are ineffective at suppressing IEEE 69 . Barid-sto{> filter Figure 5.3: Receiver with Bandstop filter for NBI suppression. 802.11a interference. Recently, an IEEE 802.11a signal was demonstrated to be modeled as a bandlimited additive white Gaussian noise [56]. In [23], the interference is first approximated using a singular value decomposition (SVD) algorithm, and it is later subtracted from the received signals, but this suppres-sion involves matrix decomposition and thus impose a heavy computational burden. The bandwidth of an IEEE 802.1 l a system is known to be 20MHz but its center frequency can be anywhere in the operating band. If the center frequency of this kind of single narrowband interferer is unknown, the two-stage adaptive filter structure discussed early can be applied to mitigate the NBI. If the center frequency is known by the receiver, a bandstop filter is proposed for interference removal. The resulting receiver is shown in Fig. 5.3. In the proposed receiver, the front-end band-stop filter will eliminate the narrow band interference IEEE 802.11a out of UWB signal band. The filtered signal then is fed to any of the equalizers discussed in Chapter 3. The advantage of this receiver structure includes complete elimination of narrow band interference, regardless of the PSD of the interferer signal. This advantage is crucial because UWB signals are restricted to very low PSD (-41.3 dBm/MHz) while IEEE 802.11a signals have a PSD that is tens of dB higher than that of the UWB signals [23]. 70 4 6 8 10 12 14 16 18 lO log^ lE^ , ) |dS| Figure 5.4: B E R versus 101og10(£b/A/V0) for MAI suppression for CM4, N = 24. 5.5 Simulation Results and Discussions In this section, we present the simulation results for multiple user interference and narrow band interference with the two-stage widely linear adaptive filter. 5.5 .1 M A I Suppression The CSI of the desired user is assumed known at the receiver, and the desired user's communication is interfered with by one BPSK DS-UWB user. The spreading code for the interferer is as shown in Table 3.2. Fig. 5.4 shows B E R versus 10 logw(Eb/N0) for multiple access interference for CM4, N = 24, with the interferer and the desired user having equal power. qf = 15 is used. The two-stage W L adaptive filters start with an L E with all taps. The L E is built based on the CSI of desired user. While for finite 71 T — ^ — Interferer's CSI unknown, F=32 taps by GA, Linear MMSE filter without interference suppressior ;;; O Interferer's CSI unknown, F=32 taps by GA, suppression with two-stage adaptive filter 4 6 fl 10 12 14 16 18 lO-log^/H,, ) |dB| Figure 5.5: B E R versus 101og10(E6/iVo) for MAI suppression for CM4, N = 6. number of taps, the two-stage adaptive filers are initialized by the linear MMSE equalizer formed with fingers being selected by the GA. The step sizes used in the first stage and the second stage of the adaptive filter are 10 - 4 and 3 x 10~3, respectively. It is observed that, for both all-tap and finite-tap cases, the two-stage adaptive filter can effectively suppress multiple access interference and provide a performance very close to the case where the CSI of the interferer is known, at the cost of the extra adaptive filter structure. Comparing the performance of the case with one unknown interferer suppressed by the adaptive filter to that with the interferer known at the receiver, at low BER, we observe that the gap in power efficiency is 0.1 dB for all-tap filter and 0.2 dB for 24-tap filter. The B E R versus 101og10(^b/Ao) for multiple access interference for CM4, N = 6 is shown in Fig. 5.5. The two-stage adaptive filter, is again observed to be 72 SINR of two-stage adaptive filter for CM4 N=24 * SINR at the 2nd stage of two-stage WL adaptive Alter • - * - - SINR at the 2nd stage of two-stage linear adaptive filter SINR at the 1 st stage of two-stage WL adaptive filter . - - - SINR at the 1 st stage of two-stage linear adaptive filter SINR at the receiver without MAI suppression Number of Iterations Figure 5.6: SINR versus number of iterations for MAI suppression for CM4, N = 24 at SNR = 14dB. able to effectively suppress interference and result in good performance, for both all-tap and finite-tap. Fig. 5.6 shows SINR versus number of iterations for multiple access interfer-ence for CM4, N = 24 at SNR = 14dB. The SINR at different stages of the W L adaptive filter and the linear adaptive filter are compared in the figure. The theoretical steady-state SINRs is calculated using equation (5.3), which calculates the steady-state SINR obtained by using training sequences. We ob-serve that the theoretical and simulated steady-state SINRs coincide for this scenario. The simulated SINRs are observed to increase as the number of itera-tions increases, and only negligible changes are discovered after 500 iterations. The simulated SINR with 1000 iterations is 0.1 dB lower than the theoretical value. The theoretical SINR value is higher than the simulated SINR value because the theoretical SINR is the result of using training symbols, while the 73 SINR of two-stage adaptive filter for CM4 N=6 . . » . i . . . . . . . . . . . . 0 200 400 600 600 1000 1200 1400 1600 1600 2000 Number of Iterations Figure 5.7: SINR versus number of iterations for MAI suppression for CM4, N = 6 at SNR = 14dB. two-stage W L LMS adaptive filters do not require any training symbols. It can be observed that the W L two-stage adaptive filter achieves a higher SINR than its linear counterpart, with less computational cost. The SINR at the output of 1st stage of W L adaptive filter is very close to that of the 1st stage of the linear adaptive filter, but the SINR at the output of the 2nd stage of the W L two-stage adaptive filters is 0.13 dB higher than that of the output of the 2nd stage of the linear two-stage filters. Suppressing MAI by the W L two-stage filters leads to an SINR gain of 2.3 dB over that without MAI suppression. Similar results can be observed in Fig. 5.7, which presents SINR versus number of iterations for multiple access interference suppression for CM4, N = 6 at SNR = 14dB, qf = 50. We can observe that the employ-ment of the W L two-stage filter for MAI suppression achieves an SINR gain of 4.5 dB over that without MAI suppression. Also, the simulated steady-state 74 Figure 5.8: B E R versus 10log10(Eb/N0) for single NBI suppression for CM4, N = 24. SINR gain of the W L two-stage filter over its linear counterpart after 2000 iterations is about 0.7 dB. The above observations indicate that the W L two-stage filter structure is a good choice for MAI suppression for DS-UWB systems because: 1) it can achieve significant SINR gains at the output over equalization without MAI suppression; 2) it has a structure simpler than its linear counterpart while resulting in better performance. 5.5.2 N B I Suppression It has been shown MAI can be effectively suppressed by the two-stage adap-tive filter. We now investigate the performance of NBI interference suppression with the two-stage adaptive filter. Single narrow-band interference suppres-\ I r r Single NBI, SIR = -20dB, Linear MMSE - • - Single NBI, SIR = -20dB, iwo-atage adatpive filtei Single NBI. SIR = -10dB, Unear MMSE • Single NBI. SIR = -1 OdB, two-stage adatpive filtei Figure 5.9: BER versus 101og10(Efe/A^o) for single NBI suppression for CM4, N = 6. sion with the two-stage adaptive filter is first considered. Recall that the single narrow-band interference has a fixed bandwidth of 20 MHz. We will look at different scenarios where the center frequency is known and unknown at the receiver, respectively. We also study the worst situation narrow-band interfer-ence, with IEEE 802.11a signals occupying the entire 300 MHz bandwidth. Fig. 5.8 plots B E R versus 101og10(Eb/A /o) for a single narrow band inter-ference for CM4, iV = 24. qf = 15 is used. It is observed that random NBI (its center frequency is unknown to the receiver) has significant impact on the UWB systems and results in a poor performance at high signal-to-interference-ratio (SIR), if no interference suppression is employed. A UWB receiver with two-stage adaptive filter, on the other hand, can work well under strong narrow-band interference, even at SIR = -20dB. A similar conclusion can be drawn for scenario CM4 and N = 6, as shown in Fig. 5.9. We observe 76 10-1 10"* - 1 1 1 1 1 — 9 — worst case NBI, bandstop titer followed by MMSE filter - if — worst case NBI, bandstop filer followed by two-stage adaptive filte single NBI. SIR = -20dB, with interference suppression —B— single NBI, SIR = -10dB, with interference suppression - - - single NBI, with band-stop Alter and MMSE filter . _ . - , Linear MMSE filter, without Interference ^ N J 5 * ^ ^ ^ - . » v > ^ . . . . x ^ . . « > s s . ^ s * * ^ - : ' : ; : : : : : ; : : : : : : : ; : ; : ; : , * » X \ -~ -i i i i \ 4 6 8 10 12 14 16 lOloo^lE,/^) [dB] Figure 5.10: B E R versus 10 log10(Eb/A^o) for NBI suppression with band-stop filter for CM4, N=24. that at low SNR, two-stage adaptive filter gives a performance slightly worse than the linear MMSE equalizer, and this can be explained as follows. At low SNR, the detection errors in the first stage (nondata-aided stage) of the two-stage filter affects the detection of the data symbols. But at high SNR, the two-stage adaptive filter greatly outperforms the linear MMSE without interference suppression. Fig. 5.10 shows B E R versus 101og10(£0/-Wo) for single narrow band interfer-ence using band-stop filter for CM4, N = 24. If the center frequency of the single narrow-band interferer is known at the receiver, a band-stop filter can be employed at the front end of the receiver to completely remove the NBI, regardless of the power of the NBI. In our simulations, an order 10 Chebyshev Type I bandstop filter with 0.5 dB of peak-to-peak ripple in the passband is 77 Figure 5.11: B E R versus 10 logw(Eb/N0) for NBI suppression with band-stop filter for CM4, N = 6. used for NBI removal, and it is followed by a linear M M S E equalizer. It is observed that only a small performance degradation between this structure and the optimal case without the presence of interference. The small perfor-mance loss is due to the fact that some useful UWB signals are also removed by the bandstop filter. We also notice that employing the two-stage adaptive filter after the bandstop filter does not lead to performance improvement. As for the worst case, we observe that pre-filtering NBI using a smiple bandstop filter is an effective way to reduce the effect of NBI. At low BER, the receiver structure with a bandstop filter approach the case without NBI, within 0.8 dB for CM4 and N = 24, and 1.2 dB for CM4 and AT = 6 (Fig. 5.11). We conclude that if the center frequency of the single NBI is known, or if multiple homogeneous narrowband interferers are expected, a simple receiver structure 78 consisting of a bandstop filter followed by a linear MMSE equalizer is able to result in good performance. On the other hand, if the center frequency of a single NBI is not available at the receiver, a two-stage W L LMS adaptive filter is proposed for the NBI suppression. 79 Chapter 6 Conclusions Equalizations at the output of R A K E receivers have been employed in many papers for DS-UWB systems. The combining schemes of R A K E receivers, however, are not optimal due to the long delay spread nature of UWB chan-nels. Therefore, we have proposed developing chip rate equalization. We have also studied the channel estimation and interference suppression for DS-UWB systems. In Chapter 3, we investigated equalizations for DS-UWB systems with BPSK modulation. We also developed two finger selection schemes to capture a re-duced number of multipaths, resulting in reduced computational complexity while at the same time producing good performance. The results of our inves-tigation can be summarized as follows. • L E is suitable for low data-rate modes of DS-UWB, Non-linear equaliza-tion (DFE) provides performance slightly better than LE. • The W L processing was found to provide gain of up to 0.4 dB over LE , and these gains come at added complexity. W L E is also found to achieve a performance very close to DFE, for both low data-rate and high data-rate. W L E is recommended for implementation. • The proposed finger selection schemes can effectively capture energy with a reduced number of paths. The SA achieves performance slightly better 80 than the GA, but has a higher computational cost. Compared with R A K E receivers, the G A has the"advantage of simple structure and low computational complexity. The GA is recommended for implementation. The number of selected fingers to achieve acceptable performance was found to be 16 for low date-rate and 50 for high data-rate. The equalization schemes and finger selection schemes are performed based on the knowledge of the CSI of the desired user. In a practical implementation, the CSI is not always available and may need to be estimated by the receiver. Furthermore, the DS-UWB systems are subject to interference by other co-existing narrow-band wireless communications systems with relatively high PSD, or other DS-UWB systems. In Chapters 4 and 5, channel estimation and interference suppression for DS-UWB systems were studied. To this end, we first investigated blind channel estimation for DS-UWB systems, and the performance was compared to that obtained by channel estimation with train-ing sequences. Adaptive filters were then proposed to suppress the MAI and NBI for DS-UWB systems. The results of our investigations can be summa-rized as: • Blind detection scheme for DS-UWB yields a poor performance, due to the long delay spread nature of the UWB channels. Therefore, channel estimation with training symbols is necessary. • By utilizing training symbols, the proposed channel estimation schemes provide a good performance, while at the same time causing low imple-mentation complexity. At low data rates, the proposed channel estima-tion scheme can approach the optimal (with perfect CSI) within 1.0 dB, with 200 training symbols. Channel estimation with training symbols are appropriate because the transmission of training symbols results in negligible bandwidth wastage for the high data rates DS-UWB systems. Compared with other channel estimation methods (LS and ML) , the proposed scheme is simple to implement. • The proposed two-stage W L LMS adaptive filters can effectively suppress 81 unknown MAI and NBI and provide a negligible performance loss to the optimal case with CSI of interference being known. The proposed filters converges rapidly to the steady-state than linear adaptive filters, while yielding a higher SINR. • If the center frequency of NBI is available, we proposed a simple inter-ference suppression receiver to largely eliminate the negative effects of NBI, regardless of the PSD of the interference. Simulation results show that the proposed receiver almost perfectly with a single NBI. Even for the worst case scenario with NBI occupying the entire possible operating band, the proposed receiver can still result in a performance within 1.0 dB of the optimal case without interference. Compared with other inter-ference suppression methods for DS-UWB systems, the proposed scheme is preferred because of its simplicity. An interesting topic for further research would be to implement the two-stage adaptive filters in hardware and study the implementation-specific is-sues. Moreover, throughout this work, time-invariant channels were assumed. It would be interesting to investigate the performance of channel estimation schemes with time-varying channels. 82 Appendix A Derivation of SINRs for Equalization Schemes In this appendix, we derive the SINRs for the equalizers in Chapter 3. We first start with the derivation of SINR for linear MMSE receiver. Since the trans-mitted data signals are real, only the real part of linear MMSE filter output is of interest for the performance of the receiver. The error signal e[k — k0] is defined as e[k — k0] = a[k — ko] — Rej /^r} . The variance of the error signal is [21] at = E{(e[k - k0])2} = E{(a[k - k0] -\\fHr + r"/])2} (A.l) = a\- 2Re{fHE{a[k - k0]r} + E{(Re{fHv})2} Also, we have E{a[k-ko]r} = a2aHko, (A.2) and £{(Re{/"r}) 2 } = ia 2Re{/"HHT } + V ( H H ^ + a2I)/a2 (A3) + \fH(n^al + all)raj Define R = H H H ^ + aft. From (A.l) , (A.2) and (A.3), we can obtain °l = °l- lK^-^l + ^Re{Hj^R_1HHr(R_1)*Hfco}(T^, (A.4) 83 where a\ is the variance of the transmitted signals. Useful signal power is ( H ? R ^ f c j V 2 , then we can have S I N R - P ° W e r interference • and • noise a\ - [1 - H J R - 1 ^ ] ^ Notice that a 2 = 1 for BPSK signals. After some manipulation, the above equation can be simplified as u 1 S I N R = - = — - , (A.6) 1 — u - — 1 u where u = H f o ( H H " + ^ I ) " 1 ^ . The SINRs for other equalization schemes can be derived with similar proce-dure. After some manipulation, the SINR for D F E is derived as „ e - r - x f ^ - ' w . I2 with ( H ^ R - 1 ^ ) 2 al  [1 - H R _ 1 H f e o j S I N R D F E = v "*° (A.7) a\ = l - ^ H f o R - 1 H f e o + ^ R e { H f o R - 1 ( H H r - H 1 : g B H ^ B ) ( R - 1 ) * H ^ o } . (A.8) The SINR for widely linear MMSE is derived as [21] S I N R ™ = Hk°„ „ _, f c: (A.9) with 1 _ H f c 0 ^ H f c o M al R = H H + f I 2 N w . (A. 10) and H and Hfc0 are defined in equation (3.11). 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